Answer:
See explanation below.
Step-by-step explanation:
Let's take P as the proportion of new candidates between 30 years and 50 years
A) The null and alternative hypotheses:
H0 : p = 0.5
H1: p < 0.5
b) Type I error, is an error whereby the null hypothesis, H0 is rejected although it is true. Here, the type I error will be to conclude that there was age discrimination in the hiring process, whereas it was fair and random.
ie, H0: p = 0.5, then H0 is rejected.
Which of the equations are true identities?
[tex]m^{3}-1=(m-1)(1+m+m^{2} ) \\m^{3}-1=m+m^{2}+m^{3} -1-m-m^{2}\\ m^{3}-1=m^{3}-1[/tex]
[tex](n+3)^{2}+2n=8n+13\\n^{2}+6n+9+2n=8n+13\\ n^{2}+8n+9=8n+13[/tex]
answer: only A
Answer:
only a
Step-by-step explanation:
Suppose that four microchips in a production run of sixty are defective. A sample of six is to be selected to be checked for defects. (a) How many different samples can be chosen
Answer:
50,063,860 different samples can be chosen
Step-by-step explanation:
The order in which the microchips are chosen is not important. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
How many different samples can be chosen
We choose 6 microchips from a set of 60. So
[tex]C_{60,6} = \frac{60!}{6!(60-6)!} = 50063860[/tex]
50,063,860 different samples can be chosen
A hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring feet. The ball is started in motion from the equilibrium position with a downward velocity of feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second). Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t.
Answer:
The solution when after t seconds the ball is y feet below its rest position is y (t) =3 et ^⁻16
Step-by-step explanation:
Solution
Given that:
The hollow steel ball weight (W) = 4 pounds
We take acceleration, g. = 32 ft/sec
The mass m = W/g = 4/32
=1/8 slug
The damping constant β = 4
The starting displacement , y (0) = 0
The initial velocity y' (0) = 3
The ball stretches the spring = 1/8 feet
Now
From Hooke's Law, F =ks
here,
k = constant spring
so,
4 =k (1/8)
k= 32
Now from Newton's law,
my'' = -ky -βy'
= (1/8) y'' = -32y - 4y'
y'' = -256 y - 32 y'
y'' + 32y' + 256 = 0 this is the equation (1)
Thus,
we solve for DE (1)
The equation (auxiliary) is m² + 32m + 256 = 0
so,
m² + 16m + 16 m _ 256 =0
m (m + 16 ) + 16 (m +16) = 0
(m +16) (m + 16 ) = 0
m₁ = - 16,
m₂ = - 16
In this case, the root is known as repeated roots
Now,
The solution is y (t) = c₁e^⁻16 t + c₂ te^⁻16 t
Now, we make use of the initial condition y (0) =0
y(0) = c₁e^⁻16 (0) + c₂ (0)e^⁻16(0)
0 = c₁ e^0 + 0
c₁ = 0
Again, we apply the initial condition y' (0) = 3
y' (t)c₁e^⁻16 t (-16( + c₂ (te^⁻16 t (-16) + e^-16)
y' (t)= - 16c₁e^⁻16 t + c₂ ( -16te^ ⁻16 + e^-16)
y' (0) =- 16c₁e^⁻16 (0) + c₂ ( -16(0)e^ ⁻16 (0) + e^-16 (0))
3 = 16c₁ + c₂ (1)
So,
3 = -16(0) + c₂ (1)
c₂ = 3
Therefore, the required solution is y(t) = (0) e^⁻16 + 3 et ^⁻16
y (t) =3 et ^⁻16
How many degrees does the minute hand of a clock travel in 1 minute? What angle does an hour hand travel in 1 min?
Answer:
Step-by-step explanation:
The movement of the minute hand of the clock is circular. This means that a complete movement of the minute hand of the clock is the same as the angle formed at the center of the circle. The sum of the angles at a point is 360 degrees. The minute hand travels 360 degrees in a 60 minutes. It means that the degrees travelled in a minute is
360/60 = 6 degrees
The hour hand travels 360 degrees in 60 minutes. Therefore, the angle that the hour hand travels in 1 minute is
360/6 = 6 degrees
A wall is in the shape of a trapezium. The first level of the wall is made up of 50 bricks where as the top level has 14 bricks. If the levels differ from each other by 4 bricks, determine the number of;
(i)levels of the bricks.
(ii)bricks used to make the wall.
Answer:
i). 10 levels of the bricks
ii). 320 bricks
Step-by-step explanation:
First level contains number of bricks = 50
Second level will contain = 50 - 4 = 46 bricks
Similarly, 3rd level will contain number of bricks = 46 - 4 = 42
Therefore, sequence formed for the number of bricks in each level of the wall will be,
50, 46, 42........14
This sequence is an arithmetic sequence having,
First term 'a' = 50
Common difference 'd' = 46 - 50 = (-4)
Last term of the sequence [tex]T_{n}[/tex]= 14
i). Expression representing last term will be,
[tex]T_{n}=a+(n-1)d[/tex]
Here [tex]T_{n}[/tex] = nth term
a = first term
n = number of term (Number of level of the wall)
d = common difference
By substituting these values in the formula,
14 = 50 + (n - 1)(-4)
14 - 50 = (-4)(n - 1)
-36 = -4(n - 1)
9 = (n - 1)
n = 9 + 1
n = 10
ii). Number of bricks used in the wall = Sum of the sequence
Expression for the sum of an arithmetic sequence is,
[tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex]
[tex]S_n=\frac{10}{2}[2\times 50+(10-1)(-4)][/tex]
= 5(100 - 36)
= 320 bricks
Sebastian was in a hotel lobby and took the elevator up 7 floors to his room. Then he took the elevator down 9 floors to the parking garage. He described his movement with the expression below.
9 + (negative 7)
What is Sebastian’s error?
Sebastian should have used –9 and 7.
Sebastian should have started at zero before adding –7.
Sebastian should have switched the two addends and written Negative 7 + 9.
Sebastian should have used 0 and –9.
Answer:
Sebastian should have used –9 and 7.
Step-by-step explanation:
Sebastian went up 7 floors not down so it should be 7 and then he went down 9 floors so it should be 7-9
Answer:
A) Sebastian should have used –9 and 7.
Silicon wafers are scored and then broken into the many small microchips that will he mounted into circuits. Two breaking methods are being compared. Out of 400 microchips broken by method A, 32 are unusable because of faulty breaks. Out of 400 microchips broken by method B, only 28 are unusable. Estimate the difference between proportions of improperly broken microchips for the two breaking methods. Use a confidence coefficient of 0.95. Which method of breaking would you recommend?
Answer:
a
The estimate is [tex]- 0.0265\le K \le 0.0465[/tex]
b
Method B this is because the faulty breaks are less
Step-by-step explanation:
The number of microchips broken in method A is [tex]n_1 = 400[/tex]
The number of faulty breaks of method A is [tex]X_1 = 32[/tex]
The number of microchips broken in method B is [tex]n_2 = 400[/tex]
The number of faulty breaks of method A is [tex]X_2 = 32[/tex]
The proportion of the faulty breaks to the total breaks in method A is
[tex]p_1 = \frac{32}{400}[/tex]
[tex]p_1 = 0.08[/tex]
The proportion of the faulty to the total breaks in method B is
[tex]p_2 = \frac{28}{400}[/tex]
[tex]p_2 = 0.07[/tex]
For this estimation the standard error is
[tex]SE = \sqrt{ \frac{p_1 (1 - p_1)}{n_1} + \frac{p_2 (1- p_2 )}{n_2} } }[/tex]
substituting values
[tex]SE = \sqrt{ \frac{0.08 (1 - 0.08)}{400} + \frac{0.07 (1- 0.07 )}{400} } }[/tex]
[tex]SE = 0.0186[/tex]
The z-values of confidence coefficient of 0.95 from the z-table is
[tex]z_{0.95} = 1.96[/tex]
The difference between proportions of improperly broken microchips for the two breaking methods is mathematically represented as
[tex]K = [p_1 - p_2 ] \pm z_{0.95} * SE[/tex]
substituting values
[tex]K = [0.08 - 0.07 ] \pm 1.96 *0.0186[/tex]
[tex]K = - 0.0265 \ or \ K = 0.0465[/tex]
The interval of the difference between proportions of improperly broken microchips for the two breaking methods is
[tex]- 0.0265\le K \le 0.0465[/tex]
Please help me with this math problem
Answer:
[tex]\dfrac{39}{8}[/tex]
Step-by-step explanation:
[tex]8\dfrac{2}{3}\div 1\dfrac{7}{9}= \\\\\\\dfrac{26}{3}\div \dfrac{16}{9}= \\\\\\ \dfrac{26}{3}\times\dfrac{9}{16}= \\\\\\\dfrac{26\times 9}{3\times 16}= \\\\\\\dfrac{234}{48}= \\\\\\\boxed{\dfrac{39}{8}}[/tex]
Hope this helps!
Answer:
[tex] 4 \dfrac{7}{8} [/tex]
Step-by-step explanation:
Change each mixed numeral into a fraction.
[tex] 8 \dfrac{2}{3} \div 1 \dfrac{7}{9} = [/tex]
[tex] = \dfrac{8 \times 3 + 2}{3} \div \dfrac{1 \times 9 + 7}{9} [/tex]
[tex] = \dfrac{26}{3} \div \dfrac{16}{9} [/tex]
To divide a fraction by another fraction, multiply the first fraction by the reciprocal of the second fraction.
[tex] = \dfrac{26}{3} \times \dfrac{9}{16} [/tex]
[tex] = \dfrac{26 \times 9}{3 \times 16} [/tex]
[tex] = \dfrac{234}{48} [/tex]
[tex] = \dfrac{39}{8} [/tex]
[tex] = 4 \dfrac{7}{8} [/tex]
Let f(x)= x^3 −6x^2+11x−5 and g(x)=4x^3−8x^2−x+12. Find (f−g)(x). Then evaluate the difference when x=−3 x=−3 .
Answer: (f-g)(x)= -138
Step-by-step explanation:
if 1/2 is added to the reciprocal of a number, the result is 1 less than twice the reciprocal; of the original number. Find the number.
Answer:
n = 1
Step-by-step explanation:
Represent the number with n.
Then: reciprocal of this numer is 1/n.
1/2 added to this reciprocal comes to 1/n + 1/2, and this is equal to
2(1/n) - 1.
We must simplify this equation and solve for n:
Use the LCD 2n:
2 + n = 4 - 1, or 2 + n = 3, or n = 1.
Answer:
2/3
Step-by-step explanation:
Let x represent the number. Then its reciprocal (the reciprocal of the original number) is 1/x
1/2 + 1/x . . . . . 1/2 added to the reciprocal of a number
2/x -1 . . . . . . . 1 less than twice the reciprocal of the original number
We want these expressions to be equal:
[tex]\dfrac{1}{2}+\dfrac{1}{x}=\dfrac{2}{x}-1\\\\\dfrac{3}{2}=\dfrac{1}{x}\qquad\text{add 1-(1/x)}\\\\x=\dfrac{2}{3}\qquad\text{multiply by 2x/3}[/tex]
The original number is 2/3.
I need help urgent plz someone help me solved this problem! Can someone plz help I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
Answer:
[tex]g(2) = 4(2) + 6 = 14[/tex]
[tex]f(2) = 2(2) + 3 = 7[/tex]
[tex](g - f)(2) = 14 - 7 = 7[/tex]
problem decoded dude
thank and follow meh
I need help! Please help me
Answer:
x = 3.6
Step-by-step explanation:
By the Postulate of intersecting chords inside a circle.
[tex]x \times 5 = 3 \times 6 \\ 5x = 18 \\ x = \frac{18}{5} \\ x = 3.6 \\ [/tex]
A box contains 2 green and 3 red balls of identical size. If two balls are picked randomly, one after the other, without replacement, find the probability of picking two balls of different colors
Answer:
there is a high possibility seeing as they are the same size although there is one more red ball than there is a green ball so it would be either likely or brobaly but not definately
Step-by-step explanation:
A woman has read manga 20 times in 20 days? how many minutes would that be?
Answer:
28800 minutes
Step-by-step explanation:
1 day = 24 hours
20(24) = 480 hours
1 hour = 60 minutes
480(6) = 28800 minutes
Answer:
20 days = 28800 minutes
Step-by-step explanation:
1 day = 1440 minutes
To convert from days to minutes, you would multiply by 1440.
20 * 1440 = 28800
Solve for X. Show all work
Answer:
About 11.77 centimeters
Step-by-step explanation:
By law of sines:
[tex]\dfrac{50}{\sin 62}=\dfrac{x}{\sin 12} \\\\\\x=\dfrac{50}{\sin 62}\cdot \sin 12\approx 11.77cm[/tex]
Hope this helps!
Paolo is buying salad and pizza for a company lunch. Suppose that a bowl of salad costs $5.00, and slice of costs $2.00.Let E be the amount in dollars that Paolo spends on salad and pizza. If Paolo buys S bowls of salad and P slices of pizza, then the total amount of money he spends E can be represented by the equation _____.Now rearrange the equation you wrote above so that P is written in terms of E and S. The quantity of pizza he buys can be represented by the equation _____.Suppose Paolo has $40.00 to spend on salad and pizza; that is E = $40.00Complete the following table with values of S or P that make the equation true.To complete the first row, determine the number of pizza slices Paolo can purchase with $40.00, when the number of salad bowls he purchases is 0.Budget (Dollars) Salad (Bowls) Pizza (Slice)40.00 0 _____40.00 4 _____40.00 _____ 0
Answer:
E=5S+2PP=0.5(E-5S)[tex]\left|\begin{array}{c|c|c}$Budget (Dollars)& $Salad (Bowls) &$Pizza (Slice)\\40.00&0&20\\40.00&4&10\\40.00&8&0\end{array}\right|[/tex]
Step-by-step explanation:
Cost of a bowl of salad = $5.00
Cost of a slice of pizza = $2.00
If Paolo buys S bowls of salad and P slices of pizza, then the total amount of money he spends E can be represented by the equation:
E=5S+2PNext, we make P the subject of the equation above.
2P=E-5S
[tex]P=\dfrac{E-5S}{2} \\P=0.5(E-5S)[/tex]
Therefore, The quantity of pizza he buys can be represented by the equation:
P=0.5(E-5S)When E=$40, we are required to complete the table below.
[tex]\left|\begin{array}{c|c|c}$Budget (Dollars)& $Salad (Bowls) &$Pizza (Slice)\\40.00&0&\\40.00&4&\\40.00&&0\end{array}\right|[/tex]
When S=0, E=$40
From P=0.5(E-5S)
P=0.5(40-5(0))=20
When S=4, E=$40
P=0.5(40-5(4))
=0.5(40-20)
=0.5*20
=10
When P=0, E=$40
P=0.5(E-5S)
0=0.5(40-5S)
40-5S=0
5S=40
S=8
Therefore, the completed table is:
[tex]\left|\begin{array}{c|c|c}$Budget (Dollars)& $Salad (Bowls) &$Pizza (Slice)\\40.00&0&20\\40.00&4&10\\40.00&8&0\end{array}\right|[/tex]
g An inspector inspects large truckloads of potatoes to determine Suppose that 12 of the potatoes sampled are found to have major defects. The P-value of this test is: Group of answer choices
Complete Question
An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects prior to using the potatoes to make potato chips. Unless there is clear evidence that this proportion, p, is less than 0.10, he will reject the shipment. He will test the hypotheses
H0: p = 0.10, Ha: p < 0.10.
He selects an SRS of 100 potatoes from the over 2000 potatoes on the truck. Suppose that 6 of the potatoes sampled are found to have major defects. The P-value of this test is.......
Group of answer choices
A 0.4082
B 0.0912
C less than 0.002
D 0.0400
Answer:
Correct option is B
Step-by-step explanation:
From the question we are told that
The null hypothesis is
[tex]H_o: p = 0.10[/tex]
The alternative hypothesis is
[tex]Ha: p < 0.10.[/tex]
The sample size is n = 100
The probability of getting a potatoes that is not defected is [tex]p=0.10[/tex]
The probability of getting a defected potatoes is q = 1-p
The proportion of defected potatoes is mathematically evaluated as
[tex]\r p = \frac{6}{100} = 0.06[/tex]
The test statistics is evaluated as
[tex]t = \frac{\r p - p}{ \sqrt{ \frac{pq}{n} } }[/tex]
substituting values
[tex]t = \frac{0.06 - 0.10}{ \sqrt{ \frac{0.10(1-0.10)}{100} } }[/tex]
[tex]t = -1.333[/tex]
The p-value is 0.0912 from the z-table (you can also use excel formula )
Select the correct answer from each drop-down menu. if f(x)=x^2+2x-3 and g(x)=x^2-9, find (f/g)(4) and (f+g)(4).
Answer:
(f/g)(4) = 3
(f + g)(4) = 28
Step-by-step explanation:
(f/g) = [tex]\frac{x^2+2x-3}{x^2-9}[/tex]
(f + g) = [tex]2x^2 + 2x -12[/tex]
Simply plug in 4 for x in both equations to find you answer!
A person x inches tall has a pulse rate of y beats per minute, as given approximately by yequals600 x Superscript negative 1 divided by 3 for 30 less than or equals x less than or equals 75. What is the instantaneous rate of change of pulse rate for the following heights? (A) 39-inches (B) 71-inches What is the instantaneous rate of change of pulse rate for a 39 inch tall person?
Answer:
a) 5.13beats/min
b) 2.82 beats/min
Step-by-step explanation:
Given the pulse rate of a person modelled by the equation y = 600x^-1/3 for 30≤x≤75
If the height is 39inches, the instantaneous rate of change of pulse rate for the heights will be expressed as;
y = 600(39)^-1/3
y = {600(1/39)}/3
y = 600/39×3
y = 600/117
y ≈ 5.13beats/min
The instantaneous rate for a 39 inches tall person is 5.13 beats per min
b) For a 71inches tall person, the beat rate will be expressed as;
y = 600(71)^-1/3
y = {600(1/71)}/3
y = 600/71×3
y = 600/213
y ≈ 2.82 beats per minute
The instantaneous rate for a 71 inches tall person is 2.82 beats per min
What do you want to find out? > The rate at which Bill puts shringles on a rood. What do you know? > Bill and Chip each finished half of the roof. > Bill needs 7 hours to put the same number of shingles on the roof that Chip does in 4 hours. > For each worker, the time multiplied by the rate equals the number of shringles > Chip's rate is 30 shringles more per hour than Bill's rate. What is Chip's rate in terms of Bill's rate? Let b = Bill's rate. Chip's rate = Bill's rate (b) ( - ) ( 4 ) ( 30 ) ( 7 ) ( + )
Answer:
(a) b = (4/7)c
(b) Bill: 40 shingles/hour; Chip: 70 shingles/hour
Step-by-step explanation:
Let b and c represent Bill's and Chip's rates in shingles per hour, respectively. Then we have ...
7b = 4c
c - b = 30 . . . . shingles per hour difference in rates
(a) Bill's rate in terms of Chip's rate can be found by dividing the first equation by 7
b = (4/7)c . . . . . Bill's rate is 4/7 of Chip's rate
__
(b) To find the rates, we can multiply the second equation by 7 and substitute using the first equation:
7c -7b = 210
7c -4c = 210
c = 210/3 = 70
b = (4/7)(70) = 40
Bill's rate is 40 shingles per hour; Chip's rate is 70 shingles per hour.
1. A farmer estimates her hens will produce
3,000 dozen more eggs this year than last year.
She estimates the probability of her net profit or
loss on each dozen eggs based on her costs.
SEE EXAMPLE 1
Egg production last year: 12,000 dozen
Estimated Net Profit per Dozen Eggs
Net profit 8 6 4 2 °
8 6 4 2 0
(¢ per doz)
Probability 0.1 0.4 0.2 0.1 0.1 0.1
What is her expected profit per dozen eggs?
What is her expected profit on the total egg
production?
Answer:
Expected profit per dozen eggs = 4 ¢
Expected profit on the total egg production = 60,000 ¢
Step-by-step explanation:
Complete table as obtained online
Net Profit | 8 | 6 | 4 | 2 | 0 | -2
Probability |0.1|0.4|0.2|0.1|0.1|0.1
a) Expected profit per dozen eggs
Expected value is given as
E(X) = Σ xᵢpᵢ
xᵢ = each variable
pᵢ = probability of each variable
E(X) = (8×0.1) + (6×0.4) + (4×0.2) + (2×0.1) + (0×0.1) + (-2×0.1) = 4 ¢ per dozen
b) Expected profit on the total egg production
Last year, she had 12,000 dozen eggs
This year, she estimates 3,000 dozen more eggs
Estimated Total egg production this year = 12000 + 3000 = 15,000 dozen eggs
Expected profit per dozen eggs = 4 ¢
Expected profit on 15,000 dozen eggs = 15000 × 4 = 60,000 ¢
Hope this Helps!!!!
Tickets for a school event were $2.75 for students and $3.25 for parents. If a total of 67 tickets were sold for
$202.25, how many student and parent tickets were sold?
There were student tickets sold and parent tickets sold.
Answer:
Parents = 36
Sudents = 31
Step-by-step explanation:
x + y = 67............ (1)
x = 67 - y
2.75x + 3.25y = 202.25
2.75 (67-y) + 3.25y = 202.25
184.25 - 2 75y + 3.25y = 202.25
0.5y = 18
y = 36
From (1)
x + 36 = 67
x = 67-36 = 31
Determine whether the distribution is a probability distribution. x 0 1 2 3 4 5 P(x) StartFraction 1 Over 25 EndFraction one fifth one half three fourths StartFraction 1 Over 50 EndFraction StartFraction 1 Over 100 EndFraction Is the probability distribution a discrete distribution? Why? Choose the correct answer below. A. No comma because some of the probabilities have values greater than 1 or less than 0. B. Yes comma because the distribution is symmetric. C. Yes comma because the probabilities sum to 1 and are all between 0 and 1 comma inclusive. D. No comma because the total probability is not equal to 1. Click to select your answer and then click Check Answer.
Answer:
D. No comma because the total probability is not equal to 1.
Step-by-step explanation:
Given the distribution:
[tex]\left|\begin{array}{c|cccccc}x&0&1&2&3&4&5\\ P(x)&1/25&1/5&1/2&3/4& 1/50&1/100\end{array}\right|[/tex]
The sum of the probabilities
[tex]\sum P(x)=1/25+1/5+1/2+3/4+ 1/50+1/100\\\sum P(x) =1.52 \neq 1[/tex]
Therefore, the distribution is not a probability distribution because the total probability is not equal to 1.
The correct option is D.
Find the slope of the line through the following points
(12,2) and (-7,5)
m =
Answer:
[tex]-\frac{3}{19}[/tex]
Step-by-step explanation:
In order to find the slope, use the following formula: [tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
The components in this equation represent y from both of the points and x from both of the points. Let's make coordinate (12, 2) #1 and coordinate (-7, 5) #2.
Plug in their corresponding numbers into the formula like so: [tex]m=\frac{5-2}{-7-12}[/tex]
Simplify: [tex]m=\frac{3}{-19}[/tex]
Help I need help please
a) Negative correlation
Negative correlation corresponds to points that move down as you go from left to right on the scatter plot.
b) Positive correlation
Positive correlation corresponds to points that move up as you go from left to right on the scatter plot.
c) No correlation
Scattered points on the scatter plot make no relationship.
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. Suppose a sample of 1537 tenth graders is drawn. Of the students sampled, 1184 read above the eighth grade level. Using the data, construct the 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level.
Answer:
The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.2087, 0.2507).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
Suppose a sample of 1537 tenth graders is drawn. Of the students sampled, 1184 read above the eighth grade level. So 1537 - 1184 = 353 read at or below this level. Then
[tex]n = 1537, \pi = \frac{353}{1537} = 0.2297[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2297 - 1.96\sqrt{\frac{0.2297*0.7703}{1537}} = 0.2087[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2297 + 1.96\sqrt{\frac{0.2297*0.7703}{1537}} = 0.2507[/tex]
The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.2087, 0.2507).
Consider a binomial experiment with n = 4 trials where the probability of success on a single trial is p = 0.25. (For each answer, enter a number. Round your answers to three decimal places.) (a) Find P(r = 0). (b) Find P(r ≥ 1) by using the complement rule.
Answer:
(a) [tex]\approx[/tex] 0.32
(b) [tex]\approx[/tex] 0.68
Step-by-step explanation:
It is given that a binomial experiment is carried out.
n = 4 trials
Probability of success, p = 0.25
We know that in a binomial experiment:
Probability of success + Probability of failure = 1
p + q = 1
So, q = 1 - 0.25 = 0.75
Probability of 'r' number of successes in 'n' trials of a binomial experiment is given as:
[tex]P(r=x) = _nC_x\times p^x(q)^{n-x}[/tex]
(a) P(r = 0) = ?
Putting values of x = 0, p and q:
[tex]P(r=0) = _4C_0\times (0.25)^0\times (0.75)^{4-0}\\P(r=0) = 1\times 1\times (0.75)^{4}\\P(r=0) \approx 0.32[/tex]
(b) Find P(r ≥ 1) = ?
Using complement rule:
P(r =0 ) + P(r ≥ 1) = 1
0.32 + P(r ≥ 1) = 1
P(r ≥ 1) = 1 - 0.32
P(r ≥ 1) = 0.68
So, the answer are:
(a) [tex]\approx[/tex] 0.32
(b) [tex]\approx[/tex] 0.68
In binomial experiment with 4 trials, Probabilities shown below.
[tex]P(r=0)=0.32[/tex] and [tex]P(r\geq 1)=0.68[/tex]
The Probability of r number of successes in n trials is given by a binomial expression,
[tex]P(X=r)=^{n}C_{r}q^{n-r}p^{r}[/tex]
Where p represent probability of success and q represent probability of unsuccessful.
Number of trials, n = 4
Probability of success, p = 0.25 and q = 1 - 0.25 = 0.75
[tex]P(r=0)=^{4}C_{0}(0.75)^{4}(0.25)^{0}=1*(0.75)^{4}*1=0.32[/tex]
[tex]P(r\geq 1)=1-P(r=0)\\\\P(r\geq 1)=1-0.32=0.68[/tex]
Learn more about binomial expression here :
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Answer:
a. 3
b. -22
c. -2
d. -2
e. 5a + 8
f. a² + 6a + 3
Step-by-step explanation:
Calculate the answers by substituting the values inside of the parenthesis for 'x':
a. f(1) = 5(1) - 2 = 3
b. f(-4) = 5(-4) - 2 = -22
c. g(-3) = (-3)² + 2(-3) - 5 = 9 - 6 - 5 = -2
d. g(1) = 1² + 2(1) - 5 = 1 + 2 -5 = -2
e. f(a+ 2) = 5(a+2) - 2 = 5a + 10 - 2 = 5a + 8
f. g(a + 2) = (a + 2)² + 2(a + 2) - 5 = a² + 4a + 4 + 2a + 4 - 5 =
a² + 6a + 3
A report on consumer financial literacy summarized data from a representative sample of 1,570 adult Americans. Based on data from this sample, it was reported that over half of U.S. adults would give themselves a grade of A or B on their knowledge of personal finance. This statement was based on observing that 820 people in the sample would have given themselves a grade of A or B.
Required:
a. Construct and interpret a 95% confidence interval for the proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance.
b. Is the confidence interval from part (a) consistent with the statement that a majority of adult Americans would give themselves a grade of A or B? Explain why or why not. Because this confidence interval , the interval consistent with the statement that a majority of adult Americans would give themselves a grade of A or B.
Answer:
a) 95% confidence interval for the proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance = (0.498, 0.547)
This means we are 95% confident that the true proportion all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is within the range 49.8% and 54.7%.
b) The confidence interval from part (a) is consistent with the statement that a majority of adult Americans would give themselves a grade of A or B because the interval obtained contains proportions that are greater than 50% indicating that there is significant evidence that the true proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is more than half of the total population.
Step-by-step explanation:
Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample proportion) ± (Margin of error)
Sample proportion = (820/1570) = 0.5223
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error)
Critical value at 95% confidence interval for sample size of 1570 is obtained from the z-tables.
Critical value = 1.960
Standard error of the mean = σₓ = √[p(1-p)/n]
p = sample proportion = 0.5223
n = sample size = 1570
σₓ = √(0.5223×0.4777/1570) = 0.0126063049 = 0.01261
95% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]
CI = 0.5223 ± (1.96 × 0.01261)
CI = 0.5223 ± 0.02471
95% CI = (0.4975916424, 0.5470083576)
95% Confidence interval = (0.4976, 0.5470)
We are 95% confident that the true proportion all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is within the range 49.8% and 54.7%.
b) The confidence interval from part (a) is consistent with the statement that a majority of adult Americans would give themselves a grade of A or B because the interval obtained contains proportions that are greater than 50% indicating that there is significant evidence that the true proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is more than half of the total population.
Hope this Helps!!!!
There are 7 times as many female students as male students at a university. What fraction of the university are female
Let’s give total students a number. Let’s say there are 800 total students
Men = x
Women = 7x. ( 7 times more)
Together there are 8x students.( 7x + x)
We have 8 x = 800
Divide both sides by 8
X = 100
100 men
700 women
Now find the fraction which is number of women / total students = 700/800 = 7/8
7/8 of the students are women.
