Question 1

A random sample of size 1,000 is taken from a population where p = .20. Find P(  < .22).
A) .2643
B) .9431
C) .9207
D) .0571

Accepted Answer

z = (.22 − .20)/= .02/.01265 = 1.5811
P(< .22) = .9431

Question 2

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. Find P(  < 51.5).
A) .9641
B) .0359
C) .1389
D) .9999

Accepted Answer

z = (51.5 − 50)/(5/) = 1.5/.833 = 1.8
P(< 51.5) = .9641

Question 3

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of .2 inches. A sample of 4 metal sheets is randomly selected from a batch. What is the probability that the average length of a sheet is between 30.25 and 30.35 inches long?
A) .9773
B) .0227
C) .0386
D) .0214

Accepted Answer

P[(30.25 − 30.05)/(.2/) ≤ z ≤ (30.35 − 30.05)/(.2/√4)] = P(2 ≤ z ≤ 3)
= .99865 − .9772 = .02145

Question 4

The number of defectives in 10 different samples of 50 observations each is the following: 5, 1, 1, 2, 3, 3, 1, 4, 2, 3. What is the estimate of the population proportion of defectives?
A) .25
B) .50
C) .05
D) .42

Accepted Answer

P ===.05

Question 5

A random sample of size 1,000 is taken from a population where p = .20. Find P(  > .21).
A) .2146
B) .0239
C) .9761
D) .7852

Accepted Answer

z = (.21 − .20)/= .01/.01265 = .7906
P(> .21) = 1.00 − .7854 = .2146

Question 6

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of .3 inches. What is the probability that the average length of a steel sheet from a sample of 9 steel sheets is more than 29.95 inches long?
A) .4602
B) .8413
C) .1587
D) .5397

Accepted Answer

P[z > (29.95 − 30.05)/(.3/)] = P(z > −1) = 1.00 − .1587 = .8413

Question 7

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. Find P(  < 48).
A) .0082
B) .8330
C) .0999
D) .1389

Accepted Answer

z = (48 − 50)/(5/) = −2.0/.833 = −2.40
P(< 48) = .0082

Question 8

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of .2 inches. What is the probability that a randomly selected sample of 4 sheets will have an average length of less than 29.9 inches long?
A) .0668
B) .9332
C) .0014
D) .4404

Accepted Answer

P[z ≤ (29.90 − 30.05)/(.2/)] = P(z ≤ −1.5) = .0668

Question 9

The number of defectives in 10 different samples of 100 observations each is the following: 1, 2, 1, 0, 2, 3, 1, 4, 2, 1. What is the estimate of the population proportion of defectives?
A) .017
B) .17
C) .016
D) .16

Accepted Answer

P ===.017

Question 10

A random sample of size 1,000 is taken from a population where p = .20. What is  ?
A) .006
B) .20
C) .02
D) .16

Accepted Answer

= ρ = .20

Question 11

Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 ounces and a standard deviation of .3 ounces. The weights of the sugar packages are normally distributed. What is the probability that 9 randomly selected packages will have an average weight in excess of 16.025 ounces?
A) .5987
B) .0062
C) .4013
D) .9938

Accepted Answer

P(z > [(16.025 − 16)/(.3] = P(z > .25) = 1.00 − .5987 = .4013

Question 12

Suppose that 60 percent of the voters in a particular region support a candidate. Find the probability that a sample of 1,000 voters would yield a sample proportion in favor of the candidate within 4 percentage points of the actual proportion.
A) .0155
B) .9952
C) .9484
D) .9902

Accepted Answer

σ_P == .0155 z = .04/.0155 = 2.58 P = .9951 − .0049 = .9902

Question 13

A random sample of size 1,000 is taken from a population where p = .20. Find P(  > .175).
A) .9759
B) .0239
C) .0392
D) .9999

Accepted Answer

z = (.175 − .20)/√(.2 × .8/1000) = −.025/.01265 = −1.9764
P(> .175) = 1.00 − .0241 = .9759

Question 14

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. Find P(  > 50.5).
A) .0002
B) .7257
C) .2743
D) .1389

Accepted Answer

z = (50.5 − 50)/(5/) = .5/.833 = .6
P(> 50.5) = 1.00 − .7257 = .2743

Question 15

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. Find P(  > 49).
A) .8331
B) .1151
C) .8849
D) .1389

Accepted Answer

z = (49 − 50)/(5 /) = −1/.833 = −1.20
P(> 49) = 1.00 − .1151 = .8849

Question 16

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. What is μ_x? A) 50 B) 5 C) 8.33 D) .833

Accepted Answer

μ_x = μ = 50

Question 17

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. What is  ?
A) .1389
B) 5
C) 8.33
D) .833

Accepted Answer

== .833

Question 18

Suppose that 60 percent of the voters in a particular region support a candidate. Find the probability that a sample of 1,000 voters would yield a sample proportion in favor of the candidate within 2 percentage points.
A) .9015
B) .8033
C) .0155
D) .7939

Accepted Answer

σ_P == .0155 z = .02/.0155 = 1.2910 P = .9016 − .0984 = .8033

Question 19

A random sample of size 1,000 is taken from a population where p = .20. Find P(  < .18).
A) .9429
B) .0569
C) .2643
D) .0793

Accepted Answer

z = (.18 − .20)/√(.2 × .8/1000) = −.02/.01265 = −1.581
P(< .18) = .0569

Question 20

A random sample of size 1,000 is taken from a population where p = .20. What is  ?
A) .0051
B) .03162
C) .01414
D) .01265

Accepted Answer

== .01265

Quiz 8: Sampling Distributions

A random sample of size 1,000 is taken from a population where p = .20. Find P( < .22) .

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. Find P( < 51.5) .

The number of defectives in 10 different samples of 50 observations each is the following: 5, 1, 1, 2, 3, 3, 1, 4, 2, 3. What is the estimate of the population proportion of defectives?

A random sample of size 1,000 is taken from a population where p = .20. Find P( > .21) .

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of .3 inches. What is the probability that the average length of a steel sheet from a sample of 9 steel sheets is more than 29.95 inches long?

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. Find P( < 48) .

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of .2 inches. What is the probability that a randomly selected sample of 4 sheets will have an average length of less than 29.9 inches long?

The number of defectives in 10 different samples of 100 observations each is the following: 1, 2, 1, 0, 2, 3, 1, 4, 2, 1. What is the estimate of the population proportion of defectives?

A random sample of size 1,000 is taken from a population where p = .20. What is ?

Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 ounces and a standard deviation of .3 ounces. The weights of the sugar packages are normally distributed. What is the probability that 9 randomly selected packages will have an average weight in excess of 16.025 ounces?

Suppose that 60 percent of the voters in a particular region support a candidate. Find the probability that a sample of 1,000 voters would yield a sample proportion in favor of the candidate within 4 percentage points of the actual proportion.

A random sample of size 1,000 is taken from a population where p = .20. Find P( > .175) .

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. Find P( > 50.5) .

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. Find P( > 49) .

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. What is μ_x?

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. What is ?

Suppose that 60 percent of the voters in a particular region support a candidate. Find the probability that a sample of 1,000 voters would yield a sample proportion in favor of the candidate within 2 percentage points.

A random sample of size 1,000 is taken from a population where p = .20. Find P( < .18) .

A random sample of size 1,000 is taken from a population where p = .20. What is ?

Quiz 8: Sampling Distributions

A random sample of size 1,000 is taken from a population where p = .20. Find P( < .22) .

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. Find P( < 51.5) .

The number of defectives in 10 different samples of 50 observations each is the following: 5, 1, 1, 2, 3, 3, 1, 4, 2, 3. What is the estimate of the population proportion of defectives?

A random sample of size 1,000 is taken from a population where p = .20. Find P( > .21) .

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of .3 inches. What is the probability that the average length of a steel sheet from a sample of 9 steel sheets is more than 29.95 inches long?

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. Find P( < 48) .

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of .2 inches. What is the probability that a randomly selected sample of 4 sheets will have an average length of less than 29.9 inches long?

The number of defectives in 10 different samples of 100 observations each is the following: 1, 2, 1, 0, 2, 3, 1, 4, 2, 1. What is the estimate of the population proportion of defectives?

A random sample of size 1,000 is taken from a population where p = .20. What is ?

Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 ounces and a standard deviation of .3 ounces. The weights of the sugar packages are normally distributed. What is the probability that 9 randomly selected packages will have an average weight in excess of 16.025 ounces?

Suppose that 60 percent of the voters in a particular region support a candidate. Find the probability that a sample of 1,000 voters would yield a sample proportion in favor of the candidate within 4 percentage points of the actual proportion.

A random sample of size 1,000 is taken from a population where p = .20. Find P( > .175) .

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. Find P( > 50.5) .

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. Find P( > 49) .

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. What is μx?

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. What is ?

Suppose that 60 percent of the voters in a particular region support a candidate. Find the probability that a sample of 1,000 voters would yield a sample proportion in favor of the candidate within 2 percentage points.

A random sample of size 1,000 is taken from a population where p = .20. Find P( < .18) .

A random sample of size 1,000 is taken from a population where p = .20. What is ?

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. What is μ_x?