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

Answers

Answer 1

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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Answer 2

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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Related Questions

Suppose that a certain examination is to be taken by five students independently of one another, and the number of minutes required by any particular student to complete the examination has the exponential distribution for which the mean is 80. Suppose that the examination begins at 9:00 a.m.


Required:

Determine the probability that at least one of the students will complete the examination before 9:40 a.m.

Answers

If a certain examination is to be taken by five students independently of one another, and the number of minutes required by any particular student to complete the examination has the exponential distribution for which the mean is 80 and the examination begins at 9:00 a.m, then the probability that at least one of the students will complete the examination before 9:40 a.m is 80.6%.

To find the probability that at least one of the students will complete the examination before 9:40 a.m, follow these steps:

The probability that at least one of the five students will complete the examination before 9:40 a.m can be calculated by taking the complementary of the probability that none of the students complete the examination before 9:40 a.mLet X be the number of minutes it takes a student to complete the examination. Since X follows an exponential distribution with a mean of 80 minutes, the probability density function (PDF) of X is given by: f(x) = (1/80) * exp(-x/80). So, λ=1/80The probability that a single student will complete the examination before 9:40 a.m: P(X ≤ 40) = ∫₀⁴⁰ λe^(-λx) dx = [-e^(-λx)]₀⁴⁰= 1 - e^(-λ * 40)= 1 - e^(-1/2)= 0.3935Therefore, the probability that all five students complete the examination after 9:40 a.m. =P(X > 40)^5=(1-P(X≤40))⁵ = (1 - 0.3935)⁵= 0.1940 (rounded to 4 decimal places)P(at least one student completes before 9:40) = 1 - P(all five students complete after 9:40)= 1 - 0.1940= 0.8060 or 80.6%.

Therefore, the probability that at least one of the five students will complete the examination before 9:40 a.m is 0.8060 or 80.6%.

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18)Sheena is placing art trading cards in her scrapbook. She has 70 cards to place. If each page has 3 rows of 3 cards each, how many pages will it take to hold all of Sheena's art cards

Answers

Sheena will need a total of 8 pages to hold all of her art cards in her scrapbook.

To determine the number of pages needed to hold all of Sheena's art cards, we can divide the total number of cards by the number of cards that can fit on each page.

Given that each page has 3 rows and 3 cards per row, the total number of cards that can fit on each page is 3 [tex]\times[/tex] 3 = 9 cards.

Sheena has a total of 70 cards to place in her scrapbook.

To find the number of pages needed, we divide the total number of cards by the number of cards per page:

Number of pages = Total number of cards / Number of cards per page

Number of pages = 70 / 9

Dividing 70 by 9 gives us a quotient of 7 with a remainder of 7.

Since we cannot have a partial page, we need to round up to the nearest whole number.

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Storage container J has a diameter of 5. 25 and a hight of 6. 25 centimeters. Which value is closest to the volume of storage container J?


A. 51


B. 103


C. 135


D. 540

Answers

The value closest to the volume of storage container J is (C) 135.

The volume of a storage container J, we can use the formula for the volume of a cylinder:

V = πr²h

where V is the volume, r is the radius of the base, and h is the height.

Given that the diameter of container J is 5.25 cm, we can calculate the radius as half of the diameter:

r = 5.25 / 2 = 2.625 cm

Substituting the values of the radius and the height (6.25 cm) into the volume formula:

V = π × (2.625)² × 6.25

V ≈ 3.1416 × 6.890625 × 6.25

V ≈ 135.38147

Rounding to the nearest whole number, the value closest to the volume of storage container J is 135.

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The question is asking to determine the volume of a storage container with a diameter of 5.25 centimeters and a height of 6.25 centimeters. There are four answer choices given.  

The formula to calculate the volume of a cylinder is given by the expression V = πr²h

where V represents the volume, r represents the radius of the cylinder and h represents the height of the cylinder.

The problem provides us with the diameter of the cylinder, which is 5.25 cm.

The diameter is twice the length of the radius, so we can find the radius by dividing the diameter by 2.

So, r = 5.25/2 = 2.625 cm

Also, the height of the cylinder is given as 6.25 cm.

We can now substitute these values into the formula for the volume of a cylinder.

V = π × (2.625)² × 6.25 = 136.919~137 cubic cm.

Therefore, the value closest to the volume of storage container J is C. 135.  

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Many homeowners buy detectors to check for the invisible gas radon in their homes. We want to determine the accuracy of these detectors. To answer this question, university researchers placed 12 radon detectors in a chamber that exposed them to 102 picocuries per liter of radon. The detector readings were: 91.9 103.8 97.8 99.6 111.4 96.6 122.3 119.3 105.4 104.8 95.0 101.7 Assume that sigma is 9 for the population of all radon detectors. We want to determine if there is convincing evidence at the 90% confidence level that the mean reading of all detectors of this type differs from the true value 105, so our hypotheses are: Null: mu = 105, Alternative: mu does not equal 105. A significance test to answer this question was done. The test statistic was z= -0.3336 and the P-value is 0.74.

1. Describe what a type 1 error would be in this situation.

2. Calculate the probability of a type 1 error in this situation.

3. Describe what a type 2 error would be in this situation.

Answers

A type 1 error in this situation would be rejecting the null hypothesis that the mean reading of all detectors of this type is equal to 105 when, in reality, it is true.

In hypothesis testing, a type 1 error occurs when we reject the null hypothesis, which assumes no significant difference or effect, when it is actually true. In this specific scenario, the null hypothesis states that the mean reading of all detectors of this type is 105. If we commit a type 1 error, it means we incorrectly conclude that there is evidence to suggest that the mean reading differs from 105, even though it does not.

A type 1 error is essentially a false positive, where we mistakenly detect an effect or difference that doesn't exist. In the context of this study, it would mean falsely concluding that the detectors are inaccurate in measuring radon levels, despite there being no convincing evidence to support this claim.

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A study is investigating whether the average screen time per week, i.e., time (in hours) spent using electronic devices in a given week, associated with work/study is equal between students who are taking online classes (referred as Student Type 1) and students who are doing a co-op (referred as Student Type 2). Study team collects data about screen time per week (in hours) from 20 randomly selected students that are Student Type 1 and 20 randomly selected students that are Student Type 2 (i.e., total 40 students). The true population variance of screen time in Student Type 1 and in Student Type 2 populations are not known.

Answers

1. The response variable in this statistical test is the average screen time per week

2. The appropriate statistical test for this study is an independent samples t-test.

1. The response variable in this statistical test is the average screen time per week, measured in hours, for both Student Type 1 and Student Type 2. The study team collects data on screen time from 20 randomly selected students belonging to Student Type 1 and 20 randomly selected students belonging to Student Type 2, resulting in a total of 40 observations. The objective is to compare the average screen time between these two groups and determine if there is a significant difference.

2. The appropriate statistical test for this study is an independent samples t-test. The independent samples t-test is used to compare the means of two independent groups and determine if there is a statistically significant difference between them. In this case, the two groups are Student Type 1 (students taking online classes) and Student Type 2 (students doing a co-op). The study aims to determine if the average screen time per week differs significantly between these two groups. Since the true population variances are not known, an independent samples t-test is an appropriate choice as it does not assume equal variances between the groups.

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The x intercept of a parabola are -2 and 7 and the y intercept is -28

determine an equation for the parabola

determine the coordinates of the vertex

Answers

The equation for the parabola with x-intercepts at -2 and 7 and a y-intercept at -28 is y = 2(x - 2)(x - 7). The coordinates of the vertex are (4.5, -38)

To determine the equation of the parabola, we can start by using the given x-intercepts (-2 and 7) and y-intercept (-28). By plugging these values into the general form of a quadratic equation, y = a(x - h)(x - k), we can solve for the coefficient "a." Substituting the x-intercepts, we get two equations: 0 = a(-2 - h)(-2 - k) and 0 = a(7 - h)(7 - k). Using the y-intercept, we have -28 = a(0 - h)(0 - k). Solving this system of equations, we find a = 2.

The equation for the parabola is y = 2(x - 2)(x - 7), which represents a upward-opening parabola.

To find the coordinates of the vertex, we can use the formula for the axis of symmetry, x = -b / (2a). Substituting the coefficients, we have x = -(-2 + 7) / (2 * 2) = 4.5. By substituting this x-coordinate into the equation of the parabola, we can find the corresponding y-coordinate. Plugging in x = 4.5, we get y = 2(4.5 - 2)(4.5 - 7) = -38.

In summary, the equation for the parabola is y = 2(x - 2)(x - 7), and the coordinates of the vertex are (4.5, -38).

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You online store only sells one item, in either regular or deluxe version.


Because of high demand and restricted supply, you restrict each customer to buying 1 item - either buying the regular version of that item, or the deluxe version of that item, but not both.


On a typical day, you have 177 customers visit your online store. Each customer has a 0.29 chance of purchasing an item. If a customer purchases an item, there is a 9% chance they buy the regular item for $5.08 and if they do not buy the regular item, then they buy the deluxe item for $23.34.


Assume each customer makes their purchase decision independently of all other customers, and each customer has the same chance of purchasing the item.


What is your expected daily sales?

Answers

The expected daily sales for your online store are approximately $1196.28.

To calculate the expected daily sales, we need to multiply the number of customers by the probability of each customer purchasing an item and then sum up the expected sales for each type of item.

Given:

- Number of customers: 177

- Probability of a customer purchasing an item: 0.29

- Probability of buying the regular item: 0.09

- Probability of buying the deluxe item: 1 - 0.09 = 0.91

- Price of the regular item: $5.08

- Price of the deluxe item: $23.34

Let's calculate the expected daily sales:

Expected sales of regular items = Number of customers * Probability of purchasing * Probability of buying the regular item * Price of the regular item

Expected sales of deluxe items = Number of customers * Probability of purchasing * Probability of buying the deluxe item * Price of the deluxe item

Expected daily sales = Expected sales of regular items + Expected sales of deluxe items

Expected sales of regular items = 177 * 0.29 * 0.09 * $5.08 ≈ $85.74

Expected sales of deluxe items = 177 * 0.29 * 0.91 * $23.34 ≈ $1110.54

Expected daily sales = $85.74 + $1110.54 ≈ $1196.28

Therefore, the expected daily sales for your online store are approximately $1196.28.

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Webrooming, researching products online before buying them in store, has become the new norm for some consumers and contrasts with showrooming, researching products in a physical store before purchasing online. A recent study reported that most shoppers have a specific spending limit in place while shopping online. Findings indicate that men spend an average of $270 online before they decide to visit a store. Assume that the spending limit for men is normally distributed and that the standard deviation is $19.


Required:

a. What is the probability that a male spent less than $229 online before deciding to visit a store?

b. What is the probability that a male spent between $298 and $320 online before deciding to visit a store?

c. Eighty percent of the amounts spent online by a male before deciding to visit a store are less than what value?

Answers

a. The probability that a male spent less than $229 online before deciding to visit a store is approximately 1.5%.

b. The probability that a male spent between $298 and $320 online before deciding to visit a store is approximately 6.6%.

c. 80% of the amounts spent online by a male before deciding to visit a store are less than approximately $285.598.

We have,

a. To find the probability that a male spent less than $229 online before deciding to visit a store, we need to calculate the cumulative probability.

Using the normal distribution with a mean of $270 and a standard deviation of $19, we can calculate:

P(X < $229) = P(Z < (229 - 270) / 19) = P(Z < -2.158) ≈ 0.015

Therefore, the probability that a male spent less than $229 online before deciding to visit a store is approximately 0.015, or 1.5%.

b. To find the probability that a male spent between $298 and $320 online before deciding to visit a store, we can calculate the difference between the cumulative probabilities for each value.

Using the normal distribution, we have:

P($298 < X < $320) = P(X < $320) - P(X < $298)

= P(Z < (320 - 270) / 19) - P(Z < (298 - 270) / 19)

= P(Z < 2.632) - P(Z < 1.474)

≈ 0.995 - 0.929

≈ 0.066

Therefore, the probability that a male spent between $298 and $320 online before deciding to visit a store is approximately 0.066, or 6.6%.

c. To find the value below which 80% of the amounts spent online by a male before deciding to visit a store fall, we can use the inverse cumulative distribution function (also known as the Z-score).

We need to find the Z-score corresponding to the cumulative probability of 0.8:

Z = invNorm(0.8) ≈ 0.842

Now, we can use the Z-score formula to find the corresponding value:

X = mean + Z x standard deviation

= $270 + 0.842 * $19

≈ $285.598

Therefore, 80% of the amounts spent online by a male before deciding to visit a store is less than approximately $285.598.

Thus,

a. The probability that a male spent less than $229 online before deciding to visit a store is approximately 1.5%.

b. The probability that a male spent between $298 and $320 online before deciding to visit a store is approximately 6.6%.

c. 80% of the amounts spent online by a male before deciding to visit a store are less than approximately $285.598.

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Consider the equation and the graph.



2/x+4 = 3^x + 1



the approximate solution to the given equation after three iterations of successive approximations is when x is about ___



a. -35/16


b. -33/16


c. -37/16


d. -39/16

Answers

The approximate solution to the given equation after three iterations of successive approximations is when x is about -33/16.

We need to use the successive approximations method to solve the equation given in the question.

We need to start by isolating the exponent term, and then rewriting the equation in the form:

x = f(x)

where f(x) is some function of x.

The equation is: frac{2}{x+4} = 3^{x} + 1

To isolate the exponent term, we subtract 1 from both sides:

frac{2}{x+4} - 1 = 3^{x}

Now, we can rewrite this in the form:

x = g(x)

where

g(x) = frac{2}{3^{x} + 1} - 4

To use the successive approximations method, we start with an initial guess x0.

Then, we use the formula x{n+1} = g(xn) to find the next approximation.

We repeat this process until the approximations converge to a fixed value.

The number of iterations required depends on the initial guess.

The approximate solution to the given equation after three iterations of successive approximations is when x is about -33/16.

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a sphereical balloon is inflating with helium at a rate of 128pi ft^3/min. how fast is the balloon's radius increasing at the instant the radius is 4 ft

Answers

A sphereical balloon is inflating with helium at a rate of [tex]128\pi ft^3/min[/tex].The balloon's radius is increasing at a rate of 8 ft/min when the radius is 4 ft.

To find the rate at which the balloon's radius is increasing, we can use the relationship between the volume of a sphere and its radius. The volume of a sphere is given by the formula V = (4/3)πr³, where V is the volume and r is the radius.

We are given that the volume is increasing at a rate of 128π ft³/min. Taking the derivative of the volume formula with respect to time, we have dV/dt = 4πr²(dr/dt), where dV/dt represents the rate of change of volume and dr/dt represents the rate of change of the radius.

At the instant when the radius is 4 ft, we can substitute r = 4 into the equation. Solving for dr/dt, we have 128π = 4π(4)²(dr/dt), which simplifies to dr/dt = 8 ft/min.

Therefore, the balloon's radius is increasing at a rate of 8 ft/min when the radius is 4 ft.

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Ron placed a grilled cheese sandwich, a sneaker, a pinecone, and a dog collar together on a scale. The sandwich weighs 0.462 lb, the sneaker weighs 290.87 g, the pinecone weighs 0.0000453 ton, and the dog collar weighs 0.246 kg. There are 2.20462 pounds in one kilogram. How many ounces do all of these objects weigh in total

Answers

The total weight of all the objects is approximately 27.7728 ounces.

To calculate the total weight of all the objects in ounces, we need to convert each weight to a common unit (ounces) and then add them together.

Given:

- Grilled cheese sandwich: 0.462 lb

- Sneaker: 290.87 g

- Pinecone: 0.0000453 ton

- Dog collar: 0.246 kg

First, let's convert the weights to pounds:

- Grilled cheese sandwich: 0.462 lb

- Sneaker: 290.87 g = 0.641 lb (since 1 lb = 453.59237 g)

- Pinecone: 0.0000453 ton = 0.0000453 * 2000 lb = 0.0906 lb (since 1 ton = 2000 lb)

- Dog collar: 0.246 kg = 0.246 * 2.20462 lb = 0.5422 lb (since 1 kg = 2.20462 lb)

Now we can add the weights together:

Total weight = 0.462 lb + 0.641 lb + 0.0906 lb + 0.5422 lb

Total weight = 1.7358 lb

Finally, let's convert the total weight to ounces:

1 lb = 16 oz

Total weight in ounces = 1.7358 lb * 16 oz/lb

Total weight in ounces ≈ 27.7728 oz

Therefore, the total weight of all the objects is approximately 27.7728 ounces.

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Suppose the probability that a pre-schooler can ride a bike is .38. Four preschoolers are selected at random. Independence from one child to the next may be assumed. What is the probability that all 4 of them can ride a bike?

Answers

the probability that all four preschoolers selected at random can ride a bike is approximately 0.0381, or 3.81%

To calculate the probability that all four preschoolers can ride a bike, we can multiply the individual probabilities together since the events are assumed to be independent.

Let's define the following probabilities:

P(R) = Probability that a preschooler can ride a bike = 0.38

Since the preschoolers are selected at random and independence is assumed, the probability that all four of them can ride a bike is:

P(all four can ride a bike) = P(R) * P(R) * P(R) * P(R)

P(all four can ride a bike) = (0.38) * (0.38) * (0.38) * (0.38)

P(all four can ride a bike) ≈ 0.0381

Therefore, the probability that all four preschoolers selected at random can ride a bike is approximately 0.0381, or 3.81% (rounded to two decimal places).

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(CO 3) Recent test scores on the Law School Admission Test (LSAT) are normally distributed with a mean of 162.4 and a standard deviation of 15.9. What is the probability that the mean of 12 randomly selected scores is less than 161

Answers

The probability that the mean of 12 randomly selected scores is less than 161 is approximately `0.3815` or `38.15%`.

Given that the recent test scores on the Law School Admission Test (LSAT) are normally distributed with a mean of 162.4 and a standard deviation of 15.9.

We are to find the probability that the mean of 12 randomly selected scores is less than 161.

Using the formula for the sampling distribution of the sample mean, we have;`

z = (x - μ) / (σ / √n)`

Where;

x = 161

μ = 162.4

σ = 15.9n = 12.

Substituting these values into the above equation, we get:`

z = (161 - 162.4) / (15.9 / √12)`

Simplifying;`

z = -1.4 / (15.9 / 3.464)`

`z = -1.4 / 4.5978`

z = -0.305

The area to the left of the z-value is given by

P(Z < -0.305)`.Using the standard normal table, we find that `P(Z < -0.305) = 0.3815`.

Therefore, the probability that the mean of 12 randomly selected scores is less than 161 is approximately `0.3815` or `38.15%`.

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The two main ways in which marketers address the competition with their strategies are by satisfying a need better than the competition and by _____. A. offering a lower price B. positioning the product C. segmenting the market D. entering new markets

Answers

The two main ways in which marketers address the competition with their strategies are by satisfying a need better than the competition and by positioning the product . The correct option is B

What is positioning ?

Positioning is the process of forming a picture of the product in the target market's minds. To do this, a unique selling proposition (USP) must be developed that sets the product apart from the competition. A statement describing the advantages of the product and why it is superior to the competition is known as the USP.

Marketers use a variety of tools to position their products such as :

AdvertisingPublic relationsSales promotion

Therefore, the correct answer is B. positioning the product.

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Answer:

offering a lower price

Step-by-step explanation:

Suppose that you and a friend are playing cards and you decide to make a friendly wager. The bet is that you will draw two cards without replacement from a standard deck. If both cards are hearts, your friend will pay you $35. Otherwise, you have to pay your friend $5. Step 1 of 2 : What is the expected value of your bet

Answers

On average, you can expect to win approximately $1.38 per bet in the long run.

To calculate the expected value of the bet, we need to consider the probabilities of each outcome and their associated payoffs.

In this scenario, there are two possible outcomes: either both cards drawn are hearts (winning the bet) or at least one of the cards is not a heart (losing the bet).

To calculate the probability of winning, we consider that the first card has a 13/52 chance of being a heart since there are 13 hearts in a standard deck of 52 cards. Then, for the second card, given that the first card was a heart, there are 12 hearts left out of the remaining 51 cards.

The probability of losing is simply the complement of the probability of winning.

Next, we consider the payoffs associated with each outcome. If both cards are hearts, the payoff is $585 (a positive value), and if at least one card is not a heart, the payoff is -$35 (a negative value).

To calculate the expected value, we multiply the probability of each outcome by its corresponding payoff. The expected value represents the average amount that can be expected to be won or lost on each bet.

By summing up the expected values of both outcomes, we obtain the overall expected value of the bet. A positive expected value indicates a favorable bet, while a negative expected value suggests an unfavorable bet.

In this case, calculating the expression ((13/52) * (12/51) * $585) + ((1 - (13/52) * (12/51)) * (-$35)) will give us the expected value of the bet, rounded to two decimal places.

To solve the expression ((13/52) * (12/51) * $585) + ((1 - (13/52) * (12/51)) * (-$35)), we'll calculate each part separately:

First, let's calculate the probability of winning the bet:

(13/52) * (12/51) = 0.0588

Now, let's calculate the probability of losing the bet:

1 - (13/52) * (12/51) = 0.9412

Next, let's calculate the expected value by multiplying the probabilities by their corresponding payoffs:

Expected value = (0.0588 * $585) + (0.9412 * (-$35))

                         = $34.3236 - $32.948

                         = $1.3756

Rounded to two decimal places, the expected value of the bet is $1.38.

Therefore, on average, you can expect to win approximately $1.38 per bet in the long run.

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Complete Question:

Suppose that you and a friend are playing cards and you decide to make a friendly wager. The bet is that you will draw two cards without replacement from a standard deck. If both cards are hearts, your friend will pay you $585. Otherwise, you have to pay your friend $35⁢.

What is the expected value of your bet? Round your answer to two decimal places. Losses must be expressed as negative values.


is
this right?
A pollster randomly selected 4 of 10 available people. How many different groups of 4 are possible? Number of possible groups 5,040 с < Prev G Search or typ

Answers

Answer:

Yes it is

Step-by-step explanation:

Out of 10 people, a random person is chosen 4 times, and every time someone is chosen the person is taken out of the "group".

That would make the equation 10 * 9 * 8 * 7 which is equal to 5040

There are 210 different groups of 4 that can be formed from a pool of 10 available people, not 5,040 as mentioned in your statement.

No, the number of possible groups of 4 is not 5,040. The correct number of different groups of 4 that can be formed from a pool of 10 available people is 210.

To calculate the number of different groups, we use the concept of combinations. The formula for combinations is given by:

nCr = n! / (r! × (n - r)!)

In this case, we have 10 available people and we want to select groups of 4. So we substitute n = 10 and r = 4 into the formula:

10C4 = 10! / (4! × (10 - 4)!)

Calculating the factorials:

10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2× 1 = 3,628,800

4! = 4 × 3 × 2 × 1 = 24

6! = 6× 5 × 4 × 3 × 2 × 1 = 720

Substituting the factorials into the formula:

10C4 = 3,628,800 / (24 ×720)

    = 3,628,800 / 17,280

    = 210

Therefore, there are 210 different groups of 4 that can be formed from a pool of 10 available people, not 5,040.

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india converts her raw score on a memory scale to a z score and finds that her score corresponds to a z score of -0.92. SHe knows her score is below the mean. What percentage of people scored lower than India on the memory scale

Answers

To find the percentage of people who scored lower than India on the memory scale, we need to calculate the cumulative probability associated with India's z-score of -0.92.

The cumulative probability represents the percentage of values that are less than or equal to a given z-score. We can use a standard normal distribution table or a statistical calculator to find this probability.

Looking up the z-score of -0.92 in a standard normal distribution table, we find that the cumulative probability associated with it is approximately 0.1788. This means that about 17.88% of the population scored lower than India on the memory scale.

Approximately 17.88% of the people scored lower than India on the memory scale, based on her z-score of -0.92. This indicates that India's score is below the mean, as she expected. The z-score provides a standardized measure that allows us to compare individual scores to the average performance in a given distribution.

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Solve using square roots. Select all correct answers.
4x² = -100


Options
-5i
10
-5
5i
-10
5

Answers

Answer:

Add

25

to both sides of the equation.

4

x

2

=

25

Divide each term in

4

x

2

=

25

by

4

and simplify.

Tap for more steps...

x

2

=

25

4

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

x

=

±

25

4

Simplify

±

25

4

.

Tap for more steps...

x

=

±

5

2

The complete solution is the result of both the positive and negative portions of the solution.

Tap for more steps...

x

=

5

2

,

5

2

Step-by-step explanation:

Sonu invested ₹ 10,000 in a business. She would be paid interest at 5% per annum

compounded annually. Find the amount credited against her name at the end of the

second year

Answers

At the end of the second year, an amount of approximately ₹ 11,025 will be credited against Sonu's name.

Sonu invested ₹ 10,000 in a business, and she will earn interest at a rate of 5% per annum compounded annually. The problem asks for the amount credited against her name at the end of the second year.

To calculate the amount credited against Sonu's name at the end of the second year, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount

P = Principal amount (₹ 10,000 in this case)

r = Annual interest rate (5% or 0.05 in decimal form)

n = Number of times interest is compounded per year (in this case, once annually)

t = Number of years (2 years in this case)

Plugging in the given values, we have:

A = ₹ 10,000(1 + 0.05/1)^(1 * 2)

Simplifying the calculation, we find:

A = ₹ 10,000(1.05)^2

A ≈ ₹ 11,025

Therefore, at the end of the second year, an amount of approximately ₹ 11,025 will be credited against Sonu's name.

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Out of 500 people surveyed, how many would you expect considered reading books or surfing the Internet as the best entertainment value

Answers

Out of the 500 people surveyed, we would expect approximately 155 of them to consider reading books or surfing the Internet as the best entertainment value.

To calculate the expected number of people who considered reading books or surfing the Internet as the best entertainment value out of the 500 surveyed, we need to calculate the percentage corresponding to reading books and surfing the Internet.

The percentage for reading books is 22% and the percentage for surfing the Internet is 9%. To find the combined percentage, we add these two percentages:

22% + 9% = 31%

Now, we can calculate the expected number by multiplying the combined percentage by the total number of people surveyed:

Expected number = 31% of 500 = (31/100) * 500 = 155

The complete question is:

Out of 500 people surveyed, how many would you expect considered reading books or surfing the Internet as the best entertainment value?

Best Entertainment Value

Type of Entertainment               Percent

Playing Interactive Games            48

Reading Books                              22

Renting Movies                              10

Going to Movie Theaters               10

Surfing the Internet                          9

Watching Television                         1

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Q8
Find the first three terms of Maclaurin series for 2 = F(x) = In (x + 3)(x+3) +

Answers

The first three terms of the Maclaurin series for the function F(x) = ln((x + 3)(x + 3)) can be found using Taylor series expansion. The Maclaurin series represents the function as an infinite sum of terms centered around x = 0.

To find the Maclaurin series for the given function F(x) = ln((x + 3)(x + 3)), we can start by taking the natural logarithm of the function. Applying the logarithmic properties, we have ln((x + 3)(x + 3)) = 2ln(x + 3). Now, we can use the Maclaurin series expansion for ln(1 + x) = x - (x^2)/2 + (x^3)/3 - ..., where the series is valid for |x| < 1.

Taking x + 3 as our new variable, we can substitute u = x + 3 into the Maclaurin series for ln(1 + x). Thus, we get ln(x + 3) = ln(u) = (u - 3) - ((u - 3)^2)/2 + ((u - 3)^3)/3 - ... = (x + 3) - ((x + 3)^2)/2 + ((x + 3)^3)/3 - ...

To find the first three terms of the Maclaurin series, we expand the expression up to the third power of (x + 3) and simplify the terms. The first three terms are F(x) = (x + 3) - ((x + 3)^2)/2 + ((x + 3)^3)/3.

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Express the terms of the following sequence by giving a recursive formula.
10, 20, 30, 40, . .

Answers

The recursive formula for an, the nth term of the sequence is a(n) = a(n - 1) + 10 where a(1) = 10

How to determine the recursive formula of the sequence

From the question, we have the following parameters that can be used in our computation:

10, 20, 30, 40, . .

The above definitions imply that we simply add 10 to the previous term to get the current term

Using the above as a guide,

So, we have the following representation

a(n) = a(n - 1) + 10

Where

a(1) = 10

Hence, the sequence is a(n) = a(n - 1) + 10 where a(1) = 10

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For the following sample of n = 8 scores: 0, 1, 1/2, 0, 3, 1/2,0,1 Simplify the arithmetic by first multiplying each score by 2 to obtain a new sample of 0, 2, 1, 0, 6, 1, 0, and 2. Then, compute the mean and standard deviation for the new sample.
Mnew -
Snew -


Using the values you just obtained, what are the values for the mean and standard deviation for the original sample?
Moriginal -
Soriginal -

Answers

The values for the mean and standard deviation for the original sample are Moriginal = 0.625 and Soriginal = 0.9661, respectively.

Compute the mean and standard deviation for the new sample.

The mean of the original sample Soriginal is 0.625.

Moriginal = 0.625.

For the given sample of n = 8 scores: 0, 1, 1/2, 0, 3, 1/2,0,1.

We have to simplify the arithmetic by first multiplying each score by 2 to obtain a new sample of 0, 2, 1, 0, 6, 1, 0, and 2. Then, we will compute the mean and standard deviation for the new sample.

The calculations are:

[tex]$\overline{x}_{\text{new}}=\frac{\sum x_{\text{new}}}{n}=\frac{0+2+1+0+6+1+0+2}{8}=1.25$$[/tex]

This implies that the mean of the new sample is 1.25.Mnew = 1.25

Now, let us calculate the standard deviation.

To do so, we have to calculate the variance of the data. The variance is the average of the squared deviation from the mean.

That is,

[tex]$\sigma_{\text{new}}^2=\frac{\sum(x_{\text{new}}-\overline{x}_{\text{new}})^2}{n-1}[/tex]

[tex]=\frac{(0-1.25)^2+(2-1.25)^2+(1-1.25)^2+(0-1.25)^2+(6-1.25)^2+(1-1.25)^2+(0-1.25)^2+(2-1.25)^2}{8-1}\\=3.7321[/tex]

This implies that the variance of the new sample is 3.7321.

Now, we calculate the standard deviation as:

[tex]$\sigma_{\text{new}}=\sqrt{3.7321}=1.9322$[/tex]

Thus, the standard deviation of the new sample is 1.9322.

Snew = 1.9322

We will use the formula for calculating the standard deviation of a new sample from an old sample, as follows:

[tex]$\sigma_{\text{old}}=\frac{\sigma_{\text{new}}}{2}=\frac{1.9322}{2}=0.9661$$[/tex]

So, the standard deviation of the original sample is 0.9661.

Soriginal = 0.9661

To find the mean of the original sample, we will use the following formula:

[tex]$\overline{x}_{\text{old}}=\frac{\overline{x}_{\text{new}}}{2}=\frac{1.25}{2}=0.625$$[/tex]

Therefore, the mean of the original sample is 0.625.

Moriginal = 0.625

Thus, the values for the mean and standard deviation for the original sample are Moriginal = 0.625 and Soriginal = 0.9661, respectively.

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tom and tres baked 163 cookies together. Tres backed 5 less than 3 times as many as tom. How many did they each bake

Answers

Tom baked 47 cookies, and Tres baked 116 cookies.

Let's assume Tom baked x cookies. According to the information given, Tres baked 5 less than 3 times as many as Tom, which can be expressed as 3x - 5.

We know that the total number of cookies baked is 163, so we can write the equation:

x + (3x - 5) = 163

Simplifying the equation:

4x - 5 = 163

Adding 5 to both sides:

4x = 168

Dividing both sides by 4:

x = 42

Therefore, Tom baked 42 cookies. Substituting this value back into the expression for Tres's cookies, we get:

3x - 5 = 3(42) - 5 = 126 - 5 = 121

So, Tres baked 121 cookies.

In conclusion, Tom baked 42 cookies, and Tres baked 121 cookies to make a total of 163 cookies.

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In one​ city, ​26% of adults smoke. In groups of size 60 of​ adults, what is the variance of the number that​ smoke? Round the answer to the nearest hundredth.

Answers

The variance of the number of adults who smoke in a group of 60 adults is approximately 11.24.

Given,

Percentage of adults who smoke in a city = 26%

Number of adults in a group = 60

We need to find the variance of the number of adults who smoke in a group of 60 adults.

Now, we know that,

Variance = npq

Where n = number of trials or sample size

p = probability of success

q = probability of failure

q = 1 - p

Here,

Number of trials = 60

Probability of success = Probability of an adult smoking = 26% = 0.26

Probability of failure = Probability of an adult not smoking

q = 1 - p = 1 - 0.26 = 0.74

Variance = npq

Variance = 60 × 0.26 × 0.74

Variance = 11.244

Variance ≈ 11.24

Rounding off to the nearest hundredth, we get,

Variance ≈ 11.24

Hence, the variance of the number of adults who smoke in a group of 60 adults is approximately 11.24.

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A store owner uses pieces of tape to paint a window advertisement. The letters are slanted at an 80° angle. What is the measure of line 1

Answers

The measure of line 1 is approximately 85.05.

To find the measure of line 1, we need to use the principles of trigonometry. In particular, we'll use the tangent function which relates the opposite side to the adjacent side of a right triangle.

Let's denote the measure of line 1 by x. Then, from the figure below, we can see that:

x/tan(80°) = 15 (1)

Here, tan(80°) is the tangent of 80 degrees.

We're given that the letters are slanted at an 80° angle.

Also, 15 is the length of line 2, which is the hypotenuse of the right triangle formed by lines 1, 2, and 3.

Therefore, to find x, we'll solve for x in equation (1).

First, we'll evaluate tan(80°) using a calculator:

tan(80°) ≈ 5.67

Substituting tan(80°) and 15 into equation (1), we get:

x/5.67 = 15

Multiplying both sides by 5.67, we have:

x = 5.67 × 15x = 85.05

Therefore, the measure of line 1 is approximately 85.05.

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A rectangular section of granite is being cut so that the length is 3 times the width. The perimeter of the section must be less than 320 inches. Which statement is true

Answers

Answer:

D.

The length of the granite must be less than 120 inches.

Let x inches be the width of the section.

If the length is 3 times the width, then the length is 3x inches.

The perimeter of the rectangle is

P= 2 (width+length)

Hence P= 2(x+3x)

=2(4x)

=8x

Hence,

The perimeter of the section must be less than 320 inches, so

8x<320

x<40

3x<120

Therefore, The length of the granite must be less than 120 inches.

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Question

"A rectangular section of granite is being cut so that the length is 3 times the width. The perimeter of the section must be less than 320 inches.

Which statement is true?

A. The length of the granite must be at least 80 inches.

B. The length of the granite must be less than 100 inches.

C. The length of the granite must be at least 100 inches.

D. The length of the granite must be less than 120 inches."

In many situations, the distribution of the population of all possible sample means looks, at least roughly, like a ______________________________.

Answers

In many situations, the distribution of the population of all possible sample means looks, at least roughly, like a normal distribution, also known as a Gaussian distribution.

The central limit theorem plays a fundamental role in explaining this phenomenon. According to the central limit theorem, when random samples are drawn from a population with any distribution (regardless of whether the population distribution is normal or not), as the sample size increases, the distribution of the sample means tends to approximate a normal distribution.

This means that if we repeatedly take samples from a population and calculate the means of those samples, the distribution of those sample means will be bell-shaped and symmetric, resembling a normal distribution. The larger the sample size, the closer the distribution of the sample means will be to a perfect normal distribution.

The normal distribution is characterized by its bell-shaped curve, with the mean, median, and mode all located at the center. It is defined by its mean and standard deviation, where the mean represents the center of the distribution, and the standard deviation determines the spread or variability of the data.

The normal distribution is widely applicable in various fields, including statistics, social sciences, natural sciences, and engineering, due to its many desirable properties and the central role it plays in statistical inference and hypothesis testing.

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you are paid time and a half for each hour worked over 40 hours a week. Last week you worked for 50 hours and earned 660. what is your normal hourly salary

Answers

Your normal hourly salary is $12 per hour.

It is given that you are paid time and a half for each hour worked over 40 hours a week and you worked for 50 hours and earned $660. To find out your normal hourly salary, we need to calculate the base pay (before overtime) you earned for the first 40 hours of work and then calculate your time and a half pay for the remaining 10 hours. Let your normal hourly salary be x. So, base pay for the first 40 hours is 40x and overtime pay for the additional 10 hours is (10*1.5*x) = 15x. We know that you earned $660 in total.

Therefore, we can write the following equation: 40x + 15x = 660Simplifying the above equation we get:55x = 660 Dividing both sides by 55, we get: x = 12 Hence, your normal hourly salary is $12 per hour.

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True or false: One benefit of statistical sampling as compared to non-statistical sampling is that statistical sampling provides mathematically-sound methods to control for sampling risk.

Answers

The given statement is true

One benefit of statistical sampling compared to non-statistical sampling is that statistical sampling provides mathematically-sound methods to control for sampling risk. Statistical sampling techniques allow for the application of probability theory to estimate and control sampling errors and uncertainties.

By using statistical methods, one can determine the appropriate sample size, select samples randomly or systematically, and apply inferential statistics to make reliable inferences about the population being sampled. Non-statistical sampling, on the other hand, does not provide the same level of rigor in terms of controlling for sampling risk and may not yield reliable and representative results.

Therefore, given statement is true.

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