Approximately 4.01% of adult women have a height below 4 feet 11 inches (59 inches) while keeping the condition that average adult woman is 63.8 in with a standard deviation of 2.7 in.
To calculate the percentage of adult women who are under 4 feet 11 inches (or 59 inches), we need to convert this height to a z-score and then use the standard normal distribution.
To convert the height of 59 inches to a z-score, we use the formula:
z = (x - μ) / σ
where:
x = the given height (59 inches)
μ = the mean height (63.8 inches)
σ = the standard deviation (2.7 inches)
z = (59 - 63.8) / 2.7 ≈ -1.74
The z-score of approximately -1.74 indicates that a height of 59 inches is about 1.74 standard deviations below the mean.
Next, we need to find the percentage of the population below this z-score. We can consult a standard normal distribution table or use a calculator to find this percentage.
Looking up the z-score of -1.74 in a standard normal distribution table, we find that the corresponding area under the curve is approximately 0.0401.
Converting this to a percentage, we get:
Percentage = 0.0401 * 100 ≈ 4.01%
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How many views to fully define the following object: Group of answer choices A cylinder requires one view A sphere requires two views A typical prismatic requires three views all of the above
The minimum number of views required to fully define each object is as follows:
A cylinder: 1 view
A sphere: 2 views
A typical prismatic: 3 views
The minimum number of views required to fully define each object is as follows:
A cylinder: 1 view
A sphere: 2 views
A typical prismatic: 3 views
To fully define an object, we need to consider its shape and dimensions. The number of views required to fully define an object can vary depending on its complexity.
A cylinder requires one view: A cylinder has a circular base and a curved surface, so a single view showing the side view or the top view can fully define its shape and dimensions.
A sphere requires two views: A sphere is a perfectly symmetrical object, and it looks the same from all angles. Therefore, it requires at least two views, such as the front view and the top view, to fully define its shape and dimensions.
A typical prismatic requires three views: A prismatic object refers to a shape with flat, polygonal sides. To fully define such an object, we typically need three views: the front view, the top view, and the right-side view. These three views together provide information about the shape and dimensions of the prismatic object.
So, considering all the options you mentioned, the minimum number of views required to fully define each object is as follows:
A cylinder: 1 view
A sphere: 2 views
A typical prismatic: 3 views
Therefore, the answer would be "all of the above."
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Which type of scale would be least helpful to the researcher who wants to know how intensely respondents feel about a brand
A nominal scale would be least helpful to a researcher who wants to know how intensely respondents feel about a brand.
Nominal scales classify responses into distinct orders or markers without any essential order or numerical value. They're generally used for qualitative or categorical data where responses are mutually exclusive and there's no essential ranking or intensity associated with the orders. To measure the intensity of passions about a brand, a experimenter would need a scale that allows repliers to express their position of intensity or strength of their passions.
Nominal scales, similar as a" yea/ no" or" agree/ differ" scale, don't give the necessary granularity to capture the intensity of feelings or passions directly. They only indicate whether a replier belongs to a particular order without secerning the position of intensity. rather, ordinal or interval scales would be more applicable for landing the intensity of passions.
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Biologists stocked a lake with 500 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 3500. The number of fish tripled in the first year.
(a) Assuming that the size of the fish population satisfies the logistic equation dP/dt = kP (1 - P/K ) determine the constant k, and then solve the equation to find an expression for the size of the population after t years.
k= ?
P(t)= ?
(b) How long will it take for the population to increase to 1750 (half of the carrying capacity) ? answer in years
a) Using the logistic equation, dP/dt = kP(1 - P/K), we substitute P = 3P₀ and t = 1, resulting in 3kP₀(3500 - 3P₀) = 3P₀. Simplifying, we find k = 1 / (3500 - 3P₀), which gives us the constant k.
(b) We aim to determine how long it will take for the population to increase to 1750, which is half of the carrying capacity (K = 3500). Denoting the time taken as T, we solve for T when P(T) = 1750.
Using numerical styles like Euler's system or employing computer programs, we can compare the value of T that satisfies the equation. The process involves opting an original time( t ₀) and population size( P ₀), also iteratively calculating the population at each time step until P( T) is close to 1750.
k = 1 / (3500 - 3P₀)
3kP₀(3500 - 3P₀) = 3P₀
3kP₀(3500 - 3P₀) = dP/dt
k(3P₀)(1 - 3P₀/3500) = dP/dt
k(3P₀)(1 - 3P₀/3500) = dP/dt
dP/dt = kP(1 - P/K)
This numerical approach allows us to estimate the value of T, furnishing an approximate answer for how long it'll take for the population to reach half of the carrying capacity.
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College students average 8.9 hours of sleep per night with a standard deviation of 45 minutes. If the amount of sleep is normally distributed, what proportion of college students sleep for more than 10 hours
Approximately 0.9088 (or 90.88%) of college students sleep for more than 10 hours.
We have,
To find the proportion of college students who sleep for more than 10 hours, we can use the Z-score formula and the standard normal distribution.
First, let's calculate the Z-score for 10 hours of sleep using the formula:
Z = (X - μ) / σ
Where X is the value (10 hours), μ is the mean (8.9 hours), and σ is the standard deviation (45 minutes, or 0.75 hours).
Z = (10 - 8.9) / 0.75
Z = 1.33
Next, we need to find the proportion of the area under the standard normal distribution curve that corresponds to a Z-score of 1.33 or greater.
We can use a standard normal distribution table or a statistical calculator to find this value.
Using a standard normal distribution table, the proportion corresponding to a Z-score of 1.33 is approximately 0.9088.
Therefore,
Approximately 0.9088 (or 90.88%) of college students sleep for more than 10 hours.
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The proportion of college students sleep for more than 10 hours is 0.9088.
The proportion of college students who sleep for more than 10 hours, we can use the Z-score formula and the standard normal distribution.
To calculate the Z-score for 10 hours of sleep using the formula:
Z = (X - μ) / σ, where X is the value (10 hours), μ is the mean (8.9 hours), and σ is the standard deviation (45 minutes, or 0.75 hours).
Z = (10 - 8.9) / 0.75
Z = 1.33
Next, we need to find the proportion of the area under the standard normal distribution curve that corresponds to a Z-score of 1.33 or greater.
We can use a standard normal distribution table or a statistical calculator to find this value.
Using a standard normal distribution table, the proportion corresponding to a Z-score of 1.33 is approximately 0.9088.
Therefore, the proportion of college students sleep for more than 10 hours is 0.9088.
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A friend of ours takes the bus five days per week to her job. The five waiting times until she can board the bus are a random sample from a uniform distribution on the interval from 0 to 10 min.
a. Determine the pdf and then the expected value of the largest of the five waiting times.
b. Determine the expected value of the difference between the largest and smallest times.
c. What is the expected value of the sample median waiting time?
a. The pdf and then the expected value of the largest of the five waiting times is:
E(largest waiting time) ≈ 8333.33 minutes
b. The expected value of the difference between the largest and smallest times is:
E(difference) ≈ 7.40741 minutes
c. The expected value of the sample median waiting time is 5 minutes.
a. To determine the probability density function (pdf) of the largest waiting time, we can use the fact that the waiting times are uniformly distributed on the interval from 0 to 10 minutes. The pdf of a uniform distribution is constant within the interval and zero outside the interval.
Since the waiting times are independent and identically distributed, the probability that the largest waiting time is less than or equal to a given value x is given by the cumulative distribution function (CDF) of the uniform distribution:
CDF(x) = P(largest waiting time ≤ x) = [tex](x/10)^5[/tex]
To find the pdf, we differentiate the CDF with respect to x:
pdf(x) = d/dx(CDF(x)) = [tex]5/10^5 * x^4[/tex]
The expected value of the largest waiting time can be found by integrating the pdf multiplied by x:
E(largest waiting time) = ∫(x * pdf(x)) dx
= ∫(x *[tex](5/10^5 * x^4)) dx[/tex]
= [tex]5/10^5 * \int\ {(x^5)} \, dx[/tex]
= [tex]5/10^5 * (1/6) * x^6[/tex]
E(largest waiting time) = 5/60 * [tex](10^6)[/tex]
= 500000/60
≈ 8333.33 minutes
b. The difference between the largest and smallest waiting times can be calculated as:
Difference = largest waiting time - smallest waiting time
To find the expected value of the difference, we need to find the joint probability density function (pdf) of the largest and smallest waiting times. Since the waiting times are uniformly distributed, the joint pdf is constant within the region where the largest waiting time is greater than the smallest waiting time, and zero outside this region.
The probability that the largest waiting time is greater than a given value x and the smallest waiting time is less than a given value y can be calculated as:
P(largest waiting time > x, smallest waiting time < y) = [tex](x/10)^5 - (y/10)^5[/tex]
To find the pdf, we differentiate the joint CDF with respect to both x and y:
pdf(x, y) = [tex]d^2[/tex]/dxdy(CDF(x, y)) = [tex]5/10^5 * (5/10^5 * x^4) - (5/10^5 * y^4)[/tex]
The expected value of the difference between the largest and smallest waiting times can be found by integrating the pdf multiplied by (x - y):
E(difference) = ∫∫((x - y) * pdf(x, y)) dx dy
= ∫∫((x - y) *[tex](5/10^5 * (5/10^5 * x^4) - (5/10^5 * y^4))[/tex]) dx dy
The integration is performed over the region where x > y. The limits of integration for x are from 0 to 10, and for y, it is from 0 to x.
E(difference) ≈ 7.40741 minutes
c. The sample median waiting time can be determined by finding the median of the waiting times. Since the waiting times are uniformly distributed, the median is the midpoint of the interval from 0 to 10 minutes, which is 5 minutes.
Therefore, the expected value of the sample median waiting time is 5 minutes.
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If one group had a mean of 2.3, and the second group had a mean of 2.4, and this was statistically significant, this result could be described as:
The calculated t-value (-2.732) is more extreme than the critical t-value (-2.002).
Using a calculator or statistical software, we can calculate the pooled standard deviation as:
[tex]sp = \sqrt(((n_1-1)s_1^2 + (n_2-1)s_2^2)/(n_1+n_2-2))\\sp = \sqrt(((20-1)(2.8)^2 + (40-1)(2.4)^2)/(20+40-2)) \\sp= 2.570[/tex]
Next, we can calculate the t-statistic
[tex]t = (x_1 - x_2) / (sp \sqrt(1/n_1 + 1/n_2))\\t = (11.1 - 12.0) / (2.570 \sqrt(1/20 + 1/40)) = -2.732[/tex]
Looking up the critical t-value for a two-tailed test with 58 degrees of freedom ([tex]df = n_1 + n_2 - 2[/tex][tex]df = n_1 + n_2 - 2[/tex]), at the .05 level
[tex]t_{crit }= \pm 2.002[/tex]
we will reject the null hypothesis and conclude that there is a statistically significant difference between the experimental and control groups at the .05 level (two-tailed).
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A small hospital has 110 full-time employees. Twenty percent are out with the Norovirus. How many employees are sick and how many are healthy
Answer:
Step-by-step explanation:
total employees = 110
20% get sick= 110×20/100
= 22
so 22 employees are sick and
110-22= 88 are healthy.
g You have collected the heights (in inches) from a sample of 5 students. You find the standard deviation of heights is equal to -2.5. What does this tell you
The standard deviation of heights being reported as -2.5 is not possible. The standard deviation is a measure of dispersion or spread in a set of data, and it is always a non-negative value.
The standard deviation of heights being reported as -2.5 is not possible. The standard deviation is a measure of dispersion or spread in a set of data, and it is always a non-negative value. It represents the average amount by which individual data points in a dataset differ from the mean.
Since the standard deviation cannot be negative, it is likely that there was an error in the calculation or reporting of the value. It is important to review the calculations and confirm the accuracy of the result.
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In an upcoming election, 16 states will elect a new governor. Each state has only two candidates, a Democrat and a Republican, running for governor. Also, in each state, the polls indicate that each candidate is equally likely to win. Find the probabilities associated with the following events. a. Democrats win all 16 gubernatorial elections. b. Half of the elections are won by Democrats and the other half by Republicans.
a) The probability of Democrats winning all 16 elections is 1/65,536.
b) The probability of exactly half of the elections being won by Democrats and the other half by Republicans is 12870/65,536 .
a. The probability of Democrats winning all 16 gubernatorial elections, we need to determine the probability of a Democrat winning each individual election and then multiply those probabilities together since the events are independent.
Since each candidate is equally likely to win in each state, the probability of a Democrat winning an individual election is 1/2 (0.5).
Therefore, the probability of Democrats winning all 16 elections
= (1/2)¹⁶
= 1/2¹⁶
= 1/65,536.
b. The probability of half of the elections being won by Democrats and the other half by Republicans, we can use the concept of combinations. There are a total of 16 elections, and we want exactly 8 of them to be won by Democrats.
The number of ways to choose 8 elections out of 16 is given by the combination formula
C(16, 8) = 16! / (8! × (16-8)!)
= 12870.
Since each candidate is equally likely to win in each state, the probability of a Democrat winning an individual election is 1/2 (0.5). Similarly, the probability of a Republican winning an individual election is also 1/2 (0.5).
Therefore, the probability of exactly half of the elections being won by Democrats and the other half by Republicans
= (1/2)⁸ × (1/2)⁸ × 12870
= 1/2¹⁶ × 12870
= 12870/65,536.
So, the probability is 12870/65,536 or approximately 0.1967.
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In a state lottery, 48 balls are numbered 1 to 48, and 6 are chosen. What are your odds of winning the lottery provided you purchase a single ticket
The probability is approximately 0.000008155 or 0.0008155%.
To compute the probability of winning the million-dollar prize in the lottery, we need to determine the number of favorable outcomes (matching all six numbers) and the total number of possible outcomes.
The number of favorable outcomes is 1 because there is only one combination of six numbers that matches the numbers on your ticket.
The total number of possible outcomes can be calculated using the formula for combinations. Since there are 48 balls in the machine and 6 balls are drawn, the total number of possible outcomes is given by:
C(48, 6) = 48! / (6!(48-6)!) = 48! / (6!42!) = 12271512
Therefore, the probability of winning the million-dollar prize with a single lottery ticket is:
P(win) = favorable outcomes / total outcomes = 1 / 12271512 ≈ 0.00000008155
The complete question is:
In a certain lottery, 48 balls numbered 1 through 48 are placed in a machine and six of them are drawn at random. If the six numbers drawn match the numbers that a player had chosen, the player wins $1,000,000. If in this lottery, the order the numbers are drawn in does matter, compute the probability that you win themillion-dollar prize if you purchase a single lottery ticket.
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Tran Lee plans to set aside $4,100 a year for the next five years, earning 5 percent. What would be the future value of this savings amount? Use Exhibit 1-B. (Round your discount factor to 3 decimal places and final answer to 2 decimal places.) Future value
Future Value of Trans Lee is $104,334.40.
Future value (FV) is the value of a current asset at a future date based on an assumed rate of growth. The future value is important to investors and financial planners, as they use it to estimate how much an investment made today will be worth in the future. The future value calculator can be used to calculate the future value (FV) of an investment with given inputs of compounding periods (N), interest/yield rate (I/Y), starting amount, and periodic deposit/annuity payment per period (PMT).
Future value of the given savings amount can be calculated using the formula shown below:
FV = P(1 + i)n - 1 / i , Where P = $4,100 (the given amount), i = 5% ,n = 5.
Using the given values in the formula, we get:
FV = $4,100(1 + 0.05)5 - 1 / 0.05= $4,100(1.27628) / 0.05= $104,334.40 (rounded to 2 decimal places)
Therefore, the future value of Tran Lee's savings amount is $104,334.40.
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According to police​ sources, a car with a certain protection system will be recovered 95% of the time. If stolen cars are randomly​ selected, what is the mean and standard deviation of the number of cars recovered after being​ stolen? Round the answers to the nearest hundredth.
The mean and the standard deviation of number of cars recovered after being stolen is equal to 760 and 6.16 approximately respectively.
The total number of stolen cars 'n' = 800
The probability of recovering a car 'p' = 0.95
If 800 stolen cars are randomly selected and the probability of recovering a car is 0.95,
Calculate the mean and standard deviation of the number of cars recovered using the formulas for a binomial distribution.
Mean (μ) = np
⇒Mean (μ) = 800 × 0.95
⇒Mean (μ) = 760
Standard Deviation (σ) = √(np(1 - p))
⇒ Standard Deviation (σ) = √(800 × 0.95 × (1 - 0.95))
⇒ Standard Deviation (σ) ≈ √(800 × 0.95 × 0.05)
⇒ Standard Deviation (σ) ≈ √(38)
⇒ Standard Deviation (σ) ≈ 6.16
Therefore, the mean number of cars recovered after being stolen is approximately 760, and the standard deviation is approximately 6.16.
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The above question is incomplete, the complete question is:
According to police sources, a car with a certain protection system will be recovered 95% of the time. If 800 stolen cars are randomly selected, what is the mean and standard deviation of the number of cars recovered after being stolen? Round the answers to the nearest hundredth.
A digital transmission system has an error probability of 10-6. (a) Find the exact value of the probability of three or more errors in 106 digits (b) Find the approximate value of the probability of three or more errors in 106 digits by using the Poisson distribution approximation.
The approximate value of the probability of three or more errors in 106 digits by using the Poisson distribution approximation is 0.393.
Given data; Error probability, p = 10^(-6) Probability of no error in 10^6 digits, P(no error) = 1 - p = 1 - 10^(-6) = 0.999999
The exact value of the probability of three or more errors in 10^6 digits;
Using binomial distribution; Total number of trials, n = 10^6Probability of success, p = 10^(-6)
Probability of failure, q = 1 - p = 1 - 10^(-6) = 0.999999
The random variable x = number of errors in n trials = 0, 1, 2, 3, .... , n
The probability mass function of the binomial distribution is;
P(x) = ( nCx ) * (p^x) * (q^(n-x))
Where, nCx = n! / x! (n-x)!
P(3 or more errors) = P(x ≥ 3) = P(x = 3) + P(x = 4) + P(x = 5) + ..... + P(x = n)P(x = 3) = ( 10^6 C 3 ) * (10^(-6))^3 * (0.999999)^10^6-3P(x = 4) = ( 10^6 C 4 ) * (10^(-6))^4 * (0.999999)^10^6-4P(x = 5) = ( 10^6 C 5 ) * (10^(-6))^5 * (0.999999)^10^6-5......P(x = n) = ( 10^6 C n ) * (10^(-6))^n * (0.999999)^10^6-n
To find this probability, we need to evaluate these probabilities. But evaluating such a large number of probabilities is a very difficult task. So, we use Poisson distribution to approximate this binomial distribution. Approximate value of the probability of three or more errors in 10^6 digits by using the Poisson distribution approximation;
In Poisson distribution, λ = np
The random variable x = number of errors in n trials = 0, 1, 2, 3, ....
The probability mass function of Poisson distribution is;
P(x) = ( e^(-λ) ) * (λ^x) / x!
Here,
λ = np = 10^6 * 10^(-6) = 1P(x ≥ 3) = P(x = 3) + P(x = 4) + P(x = 5) + .....P(x) = ( e^(-1) ) * (1^x) / x!P(x = 3) = ( e^(-1) ) * (1^3) / 3! = 0.0613201P(x = 4)
= ( e^(-1) ) * (1^4) / 4! = 0.0153300P(x = 5) = ( e^(-1) ) * (1^5) / 5! = 0.003065662......P(x ≥ 3) = 0.0613201 + 0.0153300 + 0.003065662 + .....
= 1 - {P(x = 0) + P(x = 1) + P(x = 2)}
= 1 - [ ( e^(-1) ) * (1^0) / 0! + ( e^(-1) ) * (1^1) / 1! + ( e^(-1) ) * (1^2) / 2! ]
= 1 - [ ( 1 / e^1 ) + ( 1 / e^1 ) + ( 1 / 2e^1 ) ]
= 1 - [ ( 2 + 1 ) / 2.7183 ]
= 1 - 0.607
= 0.393 (approx.)
Therefore, the approximate value of the probability of three or more errors in 106 digits by using the Poisson distribution approximation is 0.393.
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Samir has a combination lock with numbers from 1 to 36. This is the type of lock that requires three numbers to be opened: turn right for the first number, left for the second number, and right for the third number. Samir remembers the first two numbers, and they are not equal; but he can't remember which one is first and which is second. Also, he has forgotten the third number. What is the greatest number of tries he must make to open the lock
The greatest number of tries Samir must make to open the lock is 36.
In order to open the combination lock, Samir needs to correctly guess three numbers in the correct order. Since Samir remembers the first two numbers but doesn't know their order, he essentially has two possibilities for the order of these numbers. Let's call the two numbers A and B.
Case 1: A is the first number and B is the second number.
If A is the first number, Samir needs to try all 36 possible values for the third number. This means he has to make 36 tries.
Case 2: B is the first number and A is the second number.
If B is the first number, Samir still needs to try all 36 possible values for the third number. Again, this means he has to make 36 tries.
Therefore, the maximum number of tries Samir must make is 36, which occurs in either case.
In both cases, Samir is guaranteed to find the correct combination within 36 tries because he will eventually guess the correct order of the first two numbers and try the correct third number.
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Identify the most critical criteria is which of the following steps in Multi-criteria analysis? Evaluate options Define scoring system Decide on criteria Set weights
The most critical criteria among the given steps in Multi-criteria analysis would be "Set weights."
Define scoring system This step involves establishing a scoring system or set of criteria to assess the performance or felicity of each volition. It defines the factors or attributes that are applicable to the decision- making process. Decide on criteria This step focuses on opting the criteria that will be used to estimate the druthers. It involves relating and defining the specific aspects or confines that are essential for the decision. Set weights This step involves assigning weights or significance to each criterion.
The weights reflect the relative significance or precedence of each criterion in relation to others. It quantifies the impact or influence of each criterion on the final decision. estimate options This step involves assessing and comparing the druthers grounded on the defined criteria and their assigned weights. It generally involves scoring or ranking each option according to how well it performs on each criterion.
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Simplify the expression and eliminate any negative exponent (s). Assume that all letters denote positive numbers. (a) X 3/2 X3/2 (b) y 1/4 y 15/4
The simplified expressions are (a) X^3 and (b) y^4.
a. To simplify the expression X^(3/2) * X^(3/2), we can use the rule of exponents that states when multiplying two powers with the same base, we add the exponents. In this case, we have X raised to the power of 3/2 multiplied by X raised to the power of 3/2, so we add the exponents: 3/2 + 3/2 = 6/2 = 3. Therefore, the simplified expression is X^3.
b. Similarly, for the expression y^(1/4) * y^(15/4), we add the exponents: 1/4 + 15/4 = 16/4 = 4. Therefore, the simplified expression is y^4.
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If 141 people attend a concert and tickets for adults cost $3.25 while tickets for children cost $1.75 and total receipts for the concert was $345.75, how many of each went to the concert
There were 69 adults and 72 children who attended the concert.
Let's assume that the number of adult tickets sold is represented by A, and the number of children tickets sold is represented by C. We have two equations based on the given information:
A + C = 141 (Equation 1)
3.25A + 1.75C = 345.75 (Equation 2)
From Equation 1, we can rewrite it as A = 141 - C and substitute it into Equation 2:
3.25(141 - C) + 1.75C = 345.75
Expanding and simplifying the equation, we get:
458.25 - 3.25C + 1.75C = 345.75
-1.5C = -112.5
C = 75
Substituting the value of C into Equation 1, we find:
A + 75 = 141
A = 66
Therefore, there were 66 adults and 75 children who attended the concert.
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In a Florida, 46 % of all automobiles have airbags, 25 % have anti-lock brakes, and 11.5 % have both. A vehicle is randomly selected from Florida. (keep 4 digits after decimal)
(a) What is the probability that a randomly selected vehicle will have either airbag or anti-lock brake?
(b) What is the probability that the selected vehicle will only have airbag?
(c) What is the probability that the selected vehicle will have neither airbag nor anti-lock brake?
(d) What is the probability that the selected vehicle will have an airbag, given that it has an anti-lock brake?
(e) Are the two events "the selected vehicle has airbag" and "the selected vehicle has anti-lock brake" disjoint?
Yes
No
(f) Are the two events "the selected vehicle has airbag" and "the selected vehicle has anti-lock brake" independent?
Yes or No?
a) Probability P (vehicle will have either airbag or anti-lock brake is) = 0.5950.
b) The probability that the selected vehicle will only have airbag is 0.3450.
c) The probability that the selected vehicle will have neither airbag nor anti-lock brake is 0.4050.
d) The probability that the selected vehicle will have an airbag, given that it has an anti-lock brake is 0.4600.
e) The two events are not Disjoint
f) The two events are not independent.
a. To find the probability that a randomly selected vehicle will have either airbag or anti-lock brake, we can use the formula: P(A ∪ B) = P(A) + P(B) - P(A ∩ B) where A is the event that the vehicle has an airbag and B is the event that the vehicle has anti-lock brakes. Plugging the values provided, we get: P(A ∪ B) = 0.46 + 0.25 - 0.115= 0.5950.
The probability that a randomly selected vehicle will have either airbag or anti-lock brake is 0.5950.
b) To find the probability that the selected vehicle will only have airbag, we can use the formula: P(A) - P(A ∩ B) where A is the event that the vehicle has an airbag and B is the event that the vehicle has anti-lock brakes. Plugging the values provided, we get: P(A) - P (A ∩ B) = 0.46 - 0.115= 0.3450.
The probability that the selected vehicle will only have airbag is 0.3450.
c) To find the probability that the selected vehicle will have neither airbag nor anti-lock brake, we can use the complement rule. The probability that a vehicle has either airbag or anti-lock brake is: P(A ∪ B) = 0.5950.
The probability that a vehicle does not have either airbag or anti-lock brake is: 1 - P (A ∪ B) = 1 - 0.5950= 0.4050
Hence, the probability that the selected vehicle will have neither airbag nor anti-lock brake is 0.4050.
d) To find the probability that the selected vehicle will have an airbag, given that it has an anti-lock brake, we can use the conditional probability formula: P(A | B) = P (A ∩ B) / P(B) where A is the event that the vehicle has an airbag and B is the event that the vehicle has anti-lock brakes. Plugging the values provided, we get: P(A | B) = P(A ∩ B) / P(B)= 0.115 / 0.25= 0.4600.
The probability that the selected vehicle will have an airbag, given that it has an anti-lock brake is 0.4600.
e) The two events "the selected vehicle has airbag" and "the selected vehicle has anti-lock brake" are not disjoint because there are vehicles that have both airbags and anti-lock brakes.
f) The two events "the selected vehicle has airbag" and "the selected vehicle has anti-lock brake" are not independent because the occurrence of one event affects the probability of the other event.
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let x1,...,xn be a random sample from ber(p). show that the method of moment es- timator and the maximum likelihood estimator, both, are equal to the sample proportion ˆp = n−1 ∑n i=1 xi.
The method of moment estimator and the maximum likelihood estimator for the parameter p in a Bernoulli distribution are both equal to the sample proportion, which is calculated as the sum of the observed values divided by the sample size.
Let's consider a random sample x1, x2, ..., xn from a Bernoulli distribution with parameter p. The random variables xi can take the value 1 with probability p and 0 with probability 1-p.
The method of moment estimator aims to estimate the parameter p by equating the sample moments to the theoretical moments. In this case, the first moment (mean) of the Bernoulli distribution is equal to p. The sample proportion, ˆp, represents the mean of the observed values in the sample. By setting the sample mean equal to the population mean, we get the method of moment estimator as ˆp.
The maximum likelihood estimator (MLE) seeks to find the parameter value that maximizes the likelihood function given the observed sample. For a Bernoulli distribution, the likelihood function is proportional to p raised to the power of the number of successes (sum of observed values) and (1-p) raised to the power of the number of failures (sample size minus the number of successes). Taking the logarithm of the likelihood function simplifies the calculation, and maximizing it with respect to p yields the MLE, which is also equal to the sample proportion, ˆp.
Therefore, both the method of moment estimator and the maximum likelihood estimator for the parameter p in a Bernoulli distribution are equal to the sample proportion ˆp = (1/n) * Σ(xi).
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In a study of perception, 148 men are tested and 20 are found to have red/green color blindness.
(a) Find a 94% confidence interval for the true proportion of men from the sampled population that have this type of color blindness.
(b) Using the results from the above mentioned survey, how many men should be sampled to estimate the true proportion of men with this type of color blindness to within 4% with 97% confidence?
(c) If no previous estimate of the sample proportion is available, how large of a sample should be used in (b)?
(a) The 94% confidence interval for the true proportion of men from the sampled population that have this type of color blindness is (0.0779, 0.1923)
(b) The sample size required to estimate the true proportion of men with this type of color blindness to within 4% with 97% confidence is 240 men
(c) The sample size required to estimate the true proportion of men with this type of color blindness to within 4% with 97% confidence is 693 men
(a) The formula for the confidence interval is:
p ± z * √[ (p * q ) / n ]
Where p = 20/148 = 0.1351q = 1 - 0.1351 = 0.8649z = 1.88 (z value for 94% confidence interval)
n = 148
The confidence interval can be calculated as:
p ± z * √[ (p * q ) / n ]0.1351 ± 1.88 * √[(0.1351 * 0.8649) / 148]0.1351 ± 0.0572.
Therefore, the 94% confidence interval for the true proportion of men from the sampled population that have this type of color blindness is (0.0779, 0.1923).
(b) The formula for sample size calculation is:
n = [(z * σ ) / E]^2
Where E = 0.04z = 2.17 (z value for 97% confidence interval)
σ = p * q = 0.1351 * 0.8649 = 0.1171
n = [(z * σ ) / E]^2= [(2.17 * √(0.1351 * 0.8649)) / 0.04]^2= 239.85
The sample size required to estimate the true proportion of men with this type of color blindness to within 4% with 97% confidence is 240 men.
(c) The formula for sample size calculation is:
n = [(z * σ ) / E]^2
Where E = 0.04z = 2.17 (z value for 97% confidence interval)
σ = 0.5 (as no previous estimate of the sample proportion is available)
n = [(z * σ ) / E]^2= [(2.17 * 0.5) / 0.04]^2= 692.12 ≈ 693
The sample size required to estimate the true proportion of men with this type of color blindness to within 4% with 97% confidence is 693 men.
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A fishing boat f is 20 km from s on a bearing of 095°c) mark the position of the fishing boat f with a cross
Given that a fishing boat F is 20 km away from S on a bearing of 095°. We have to mark the position of the fishing boat F with a cross. We have to determine the coordinates of F to mark its position.
To find the position of the fishing boat F, we have to use trigonometry, the Pythagoras theorem, and bearing.In right triangle OST: we have:SO = 20 kmOSB = 95°Using trigonometrytan(SOB) = BT / SOwhere BT = ST - BS = ST - (SO * tan(SOB))Using Pythagoras theorem:ST² = SO² + BT²ST² = 20² + (ST - 20 * tan(95°))²ST² = 400 + ST² - 40 * ST * tan(95°) + 400 * tan²(95°)ST² - ST² + 40 * ST * tan(95°) - 400 * tan²(95°) - 400 = 0
Solving the above quadratic equation using the quadratic formula:We get, ST ≈ 62.65 kmTherefore, the position of fishing boat F is approximately (x, y) = (30.54 km, 53.26 km)
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noah wrote that 6 6 = 12. then he wrote that 6 6 − n = 12 − n. select the phrases that make the statement true.
The phrases that make the statement true in the given problem "Noah wrote that 6 6 = 12.
Then he wrote that 6 6 − n = 12 − n" are:
Explanation: We are given,Noah wrote that 6 6 = 12.
(1)Then he wrote that 6 6 − n = 12 − n.
(2)Here, we have to find the phrases that make the statement true.
According to (1), Noah wrote that 6 multiplied by 6 equals 12. It is a false statement as 6 multiplied by 6 is 36, not 12.According to (2), Noah wrote that the difference between 6 multiplied by 6 and n equals the difference between 12 and n. It is a true statement as we can prove it mathematically.6 * 6 - n = 12 - n36 - n = 12 - nn = nHence, the phrases that make the statement true in the given problem are "6 6 − n = 12 − n".
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There are 6 students in an art class, made up of 4 girls and 2 boys. Four children are chosen at random to attend an art exhibit. What is the probability that at least three girls are chosen
The probability that at least three girls are chosen to attend an art exhibit is 1/3 or approximately 0.33 or 33.33%.
To find the probability that at least three girls are chosen to attend an art exhibit from an art class made up of 6 students, where 4 are girls and 2 are boys, we can use the hypergeometric distribution.
Let X be the number of girls among the four children chosen at random to attend the exhibit. We are interested in finding P(X ≥ 3).
The formula for the hypergeometric distribution is given by:
P(X = x) = [ (Cn,x) (Cm,r-x) ] / (Cn+m,r)
where:
Cn,x is the number of ways to choose x items from the n items of a certain type.
Cm,r-x is the number of ways to choose r-x items from the m items of another type.
Cn+m,r is the number of ways to choose r items from the n+m items.
Let n = 4, m = 2, and r = 4. Then, P(X ≥ 3) = P(X = 3) + P(X = 4).
P(X = 3) = [ (C4,3) (C2,1) ] / (C6,4) = 4/15
P(X = 4) = [ (C4,4) (C2,0) ] / (C6,4) = 1/15
Therefore, P(X ≥ 3) = P(X = 3) + P(X = 4) = 4/15 + 1/15 = 5/15 = 1/3.
The probability that at least three girls are chosen to attend the art exhibit is 1/3 or approximately 0.33 or 33.33%.
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round to nearest cent
The value of the account after 8 years, will be $6,645.82.
To calculate the value of Malik's account after 8 years with weekly compounding interest, we can use the formula for compound interest:
A = P(1 + r/n[tex])^{(nt)[/tex]
Where:
A is the final amount
P is the principal amount (initial deposit)
r is the annual interest rate (in decimal form)
n is the number of times interest is compounded per year
t is the number of years
Given:
P = $5000
r = 3.9% = 0.039
n = 52 (weekly compounding)
t = 8 years
Using these values, we can substitute them into the formula and calculate the final amount A:
A = 5000(1 + 0.039/52[tex])^{(52)(8)[/tex]
A ≈ $6,645.82
Therefore, the value of the account after 8 years, will be $6,645.82.
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To test a second condition only after the result of the first condition is known, ____________________ If statements can be used.
To test a second condition only after the result of the first condition is known, If statements can be used. The "else if" statement can be used to test a second condition only after the result of the first condition is known.
If statements are programming language statements that enable a computer program to make a decision on whether or not to perform a certain code block. The code within the conditional statement will only execute if the conditional expression is true. If there is a need to test a second condition only after the result of the first condition is known, one can use If statements as it allows the computer program to make decisions. An If statement checks a condition, and if the condition is true, it carries out a block of code otherwise, it skips the block and proceeds to the next block of code. A code block to be executed if the condition is true can be specified with the if statement. The conditional statement in an if statement can be used to compare two values. The two values must be of the same data type in order to be compared.
The "else if" statement can be used to test a second condition only after the result of the first condition is known.
In programming, the "if" statement is used to test a condition and execute a block of code if the condition is true. However, when we want to test multiple conditions sequentially, the "else if" statement is used. It allows us to specify an additional condition to test if the previous condition(s) evaluated to false.
Here's an example of how the "if" and "else if" statements can be used:
if (condition1) {
// code to execute if condition1 is true
} else if (condition2) {
// code to execute if condition1 is false and condition2 is true
} else {
// code to execute if both condition1 and condition2 are false
}
In this case, the "else if" statement allows us to test the second condition only if the first condition is false. It provides a way to handle multiple scenarios or options based on different combinations of conditions.
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What is the product of 4. 01 × 10-5 and 2. 56 ×108? 1. 0266 × 4 1. 0266 × 40 1. 0266 ×104 1. 0266 × 410.
The product of [tex]4.01 * 10^(-5)[/tex]and [tex]2.56 * 10^8[/tex] is 10265.6.
To find the product of [tex]4.01 * 10^(-5)[/tex] and [tex]2.56 * 10^8[/tex], we can multiply the decimal parts and add the exponents of 10.
[tex]4.01 * 10^(-5) * 2.56 * 10^8 = (4.01 * 2.56) * (10^(-5) * 10^8)[/tex]
Calculating the decimal part: 4.01 × 2.56 = 10.2656
Calculating the exponent part: [tex]10^(-5) * 10^8 = 10^(-5+8) = 10^3 = 1000[/tex]
Multiplying the decimal part and exponent part together:
10.2656 × 1000 = 10265.6
So, the product of [tex]4.01 * 10^(-5) and 2.56 * 10^8[/tex] is 10265.6.
Therefore, none of the provided options [tex](1.0266 * 4, 1.0266 * 40, 1.0266 * 10^4, 1.0266 * 410)[/tex]are correct.
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A boat heading out to sea starts out at Point A, at a horizontal distance of 1159 feet from a lighthouse/the shore. From that point, the boat's crew measures the angle of elevation to the lighthouse's beacon-light from that point to be 9º. At some later time, the crew measures the angle of elevation from point B to be 2°. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
the distance from Point A to Point B is approximately 37,407 feet.
To find the distance from Point A to Point B, we can use trigonometry and the concept of similar triangles.
Let's denote the distance from Point A to Point B as x.
From Point A, the angle of elevation to the lighthouse's beacon-light is 9°. This forms a right triangle between Point A, the lighthouse, and the beacon-light.
In this triangle, the opposite side (height) is the distance from the beacon-light to the lighthouse, and the adjacent side (base) is the horizontal distance from Point A to the lighthouse. We can use the tangent function to relate these sides:
tan(9°) = height / 1159 feet
Solving for the height, we have:
height = 1159 feet * tan(9°)
Now, consider the triangle formed by Point B, the lighthouse, and the beacon-light. The angle of elevation from Point B is 2°. This triangle is similar to the previous triangle because both triangles share the same angles.
Therefore, the ratio of the height to the horizontal distance in the second triangle will be the same as in the first triangle. Using this ratio, we can express the height in terms of the unknown distance x:
height = x * tan(2°)
Now, we can set up an equation using the derived expressions for the height:
1159 feet * tan(9°) = x * tan(2°)
Solving for x:
x = (1159 feet * tan(9°)) / tan(2°)
Calculating this expression:
x ≈ 37407 feet
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In 2017, a website reported that only 10% of surplus food is being recovered in the food-service and restaurant sector, leaving approximately 1.5 billion meals per year uneaten. Assume this is the true population proportion and that you plan to take a sample survey of 535 companies in the food service and restaurant sector to further investigate their behavior.
Required:
a. Show the sampling distribution of p, the proportion of food recovered by your sample respondents.
b. What is the probability that your survey will provide a sample proportion within ±0.015 of the population proportion?
a. The sampling distribution of p, the proportion of food recovered by your sample respondents, can be shown by normal distribution.
b. The probability that the survey will provide a sample proportion within ±0.015 of the population proportion is 65.4%.
a. Sampling distribution of p, the proportion of food recovered by your sample respondents can be shown by Normal distribution with:
μp = 10/100 = 0.10 is the mean of the sampling distribution of p.
σp = √((p(1 - p))/n) = √((0.10(0.90))/535) = 0.0186 is the standard deviation of the sampling distribution of p.
b. We have to find the probability that our survey will provide a sample proportion within ±0.015 of the population proportion, given that the sample size, n = 535, Sample proportion = p.
Sample proportion within ±0.015 of the population proportion can be written as:
0.10 - 0.015 ≤ p ≤ 0.10 + 0.015
0.085 ≤ p ≤ 0.115
Now we will transform the given equation as follows:
z = (p - μp)/σp
Lower value of z = (0.085 - 0.10)/0.0186 = -0.8065
Upper value of z = (0.115 - 0.10)/0.0186 = 0.8065
The area in between the lower and upper value of z is represented by the area under the standard normal curve. Using standard normal distribution table, the area in between -0.8065 and 0.8065 is approximately 0.654 or 65.4%.
Therefore, the probability that the survey will provide a sample proportion within ±0.015 of the population proportion is 65.4%.
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A student wants to put four distinct songs on her playlist from a collection of 55 songs. Determine the number of different ways she can do this if the order in which the songs appear does not matter.
There are 148,995 number of ways the student can put four distinct songs on her playlist from a collection of 55 songs, considering the order does not matter.
To determine the number of different ways the student can put four distinct songs on her playlist from a collection of 55 songs, we can use the concept of combinations.
Since the order in which the songs appear does not matter, we need to calculate the number of combinations.
The formula for calculating combinations is:
C(n, r) = n! / (r!(n - r)!)
Where:
C(n, r) represents the number of combinations of n items taken r at a time,
n! represents the factorial of n (the product of all positive integers less than or equal to n),
and r! represents the factorial of r.
In this case, the student wants to choose 4 songs from a collection of 55 songs.
C(55, 4) = 55! / (4!(55 - 4)!)
Simplifying the equation:
C(55, 4) = 55! / (4! * 51!)
Calculating the factorials:
55! = 55 * 54 * 53 * ... * 3 * 2 * 1
4! = 4 * 3 * 2 * 1
51! = 51 * 50 * 49 * ... * 3 * 2 * 1
Canceling out common terms:
C(55, 4) = (55 * 54 * 53 * 52) / (4 * 3 * 2 * 1)
Calculating the value
C(55, 4) = 148,995
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¿Cuánto es 60.15 entre 3?
60.15 dividido entre 3 es igual a 20.05.
