Deck 9: Sampling Distributions

Question 1

The sampling distribution of the sample means is less variable than the population distribution.

Answer 1

True

Question 2

According to the central limit theorem, if a sample of size 56 is drawn from a population with a standard deviation of 14, the standard deviation of the distribution of the sample means would equal ___.

A) 14
B) 1.87
C) 3.5
D) 0.25
E) 3.74

Answer 2

1.87

Question 3

According to the central limit theorem, for samples of size 64 drawn from a population with $\mu$ = 800 and $\sigma$ = 56, the mean of the sampling distribution of sample means would equal ___.

A) 7
B) 8
C) 100
D) 800
E) 80

Answer 3

800

Question 4

The standard deviation of a sampling distribution of the sample means is commonly called the standard error of the mean.

Question 5

Increasing the sample size causes the numerical value of standard error of the sample means to increase.

Question 6

If the population is normally distributed, the sample means of a sample of size n = 5 are normally distributed.

Question 7

According to the central limit theorem, for samples of size 64 drawn from a population with $\mu$ = 800 and $\sigma$ = 56, the standard deviation of the sampling distribution of sample means would equal ___.

A) 7
B) 8
C) 100
D) 800
E) 80

Question 8

According to the central limit theorem, if a sample of size 100 is drawn from a population with a standard deviation of 80, the standard deviation of sample means would equal ___.

A) 0.80
B) 8
C) 80
D) 800
E) 0.080

Question 9

According to the central limit theorem, if a sample of size 64 is drawn from a population with a standard deviation of 80, the standard deviation of sample means would equal ___.

A) 10.000
B) 1.250
C) 0.125
D) 0.800
E) 0.080

Question 10

The normal approximation for binomial distribution can be used when n = 10 and π =1/5.

Question 11

The mean of the sample means is the same as the mean of the population

Question 12

According to the central limit theorem, if a sample of size 100 is drawn from a population with a mean of 80, the mean of all sample means would equal ___.

A) 0.80
B) 8
C) 80
D) 100
E) 120

Question 13

Suppose 90% of students in some specific college have a computer at home and a sample of 40 students is taken. The probability that more than 30 of those in the sample have a computer at home can be approximated using the normal approximation.

Question 14

The sampling distribution of
is close to normal provided that n ≥30.

Question 15

Decreasing the sample size causes the sampling distribution of ẍ to ___.

A) shift to the right
B) shift to the left
C) have more dispersion
D) have less dispersion
E) stay unchanged

Question 16

According to the central limit theorem, if a sample of size 56 is drawn from a population with a mean of 16, the mean of all sample means would equal ___.

A) 56
B) 16
C) 7.5
D) 44.0
E) 196

Question 17

A correction for continuity must be made when approximating the binomial distribution problems using a normal distribution.

Question 18

The sampling distribution of
has a mean equal to the square root of the population proportion π.

Question 19

A sampling distribution is the distribution of a sample statistic such as the sample mean or sample proportion.

Question 20

The sampling distribution of the sample means is close to the normal distribution only if the distribution of the population is close to normal.

Question 21

A carload of steel rods has arrived at Cybermatic Construction Company. The car contains 50,000 rods. Claude Ong, manager of Quality Assurance, directs his crew measure the lengths of 100 randomly selected rods. If the population of rods has a mean length of 120 cm and a standard deviation of 0.05 cm, the probability that Claude's sample has a mean between 119.985 and 120.0125 cm is ___.

A) 0.9925
B) 0.9974
C) 0.9876
D) 0.9544
E) 0.9044

Question 22

Suppose a population has a mean of 400 and a standard deviation of 24. If a random sample of size 144 is drawn from the population, the probability of drawing a sample with a mean of more than 404.5 is ___.

A) 0.0139
B) 0.4861
C) 0.4878
D) 0.0122
E) 0.5000

Question 23

Suppose a population has a mean of 450 and a variance of 900. If a random sample of size 100 is drawn from the population, the probability that the sample mean is between 448 and 453 is ___.

A) 0.4972
B) 0.6826
C) 0.4101
D) 0.5899
E) 0.9878

Question 24

A carload of steel rods has arrived at Cybermatic Construction Company. The car contains 50,000 rods. Claude Ong, manager of Quality Assurance, directs his crew measure the lengths of 100 randomly selected rods. If the population of rods have a mean length of 120 cm and a standard deviation of 0.05 cm, the probability that Claude's sample has a mean less than 119.985 cm is ___.

A) 0.9974
B) 0.0026
C) 0.4987
D) 0.0013
E) 0.0030

Question 25

Albert Abbasi, VP of Operations at Ingleside International Bank, is evaluating the service level provided to walk-in customers. Accordingly, he plans a sample of waiting times for walk-in customers. If the population of waiting times has a mean of 15 minutes and a standard deviation of 4 minutes, the probability that Albert's sample of 64 will have a mean less than 14 minutes is ___.

A) 0.4772
B) 0.0228
C) 0.9772
D) 0.9544
E) 1.0000

Question 26

Albert Abbasi, VP of Operations at Ingleside International Bank, is evaluating the service level provided to walk-in customers. Accordingly, he plans a sample of waiting times for walk-in customers. If the population of waiting times has a mean of 15 minutes and a standard deviation of 4 minutes, the probability that Albert's sample of 64 will have a mean between 13.5 and 16.5 minutes is ___.

A) 0.9974
B) 0.4987
C) 0.9772
D) 0.4772
E) 0.5000

Question 27

Suppose a population has a mean of 870 and a variance of 1,600. If a random sample of size 64 is drawn from the population, the probability that the sample mean is between 860 and 875 is ___.

A) 0.9544
B) 0.6826
C) 0.8785
D) 0.5899
E) 0.8185

Question 28

Suppose a population has a mean of 400 and a standard deviation of 24. If a random sample of size 144 is drawn from the population, the probability of drawing a sample with a mean between 395.5 and 404.5 is ___.

A) 0.9756
B) 0.0244
C) 0.0278
D) 0.9722
E) 1.0000

Question 29

According to the central limit theorem, for samples of size 169 drawn from a population with $\mu$ = 1,014 and $\sigma$ = 65, the mean of the sampling distribution of sample means would equal ___.

A) 1,014
B) 65
C) 5
D) 6
E) 3

Question 30

A carload of steel rods has arrived at Cybermatic Construction Company. The car contains 50,000 rods. Claude Ong, manager of Quality Assurance, directs his crew measure the lengths of 100 randomly selected rods. If the population of rods has a mean length of 120 cm and a standard deviation of 0.05 cm, the probability that Claude's sample has a mean greater than 120.0125 cm is ___.

A) 0.0124
B) 0.0062
C) 0.4938
D) 0.9752
E) 1.0000

Question 31

A random sample of size 100 is drawn from a population with a standard deviation of 10. If only 5% of the time a sample mean greater than 20 is obtained, the mean of the population is ___.

A) 18.35
B) 16.25
C) 17.2
D) 20
E) 19

Question 32

Suppose the population of all colleges shows the annual parking fee per student is $110 with a standard deviation of $18. If a random sample of size 49 is drawn from the population, the probability of drawing a sample with a mean of less than $92 is ___.

A) 0.3400
B) 0.1600
C) 0.0000
D) 1.0000
E) 0.7000

Question 33

Suppose the population of all colleges shows the annual parking fee per student is $110 with a standard deviation of $18. If a random sample of size 49 is drawn from the population, the probability of drawing a sample with a mean of more than $115 is ___.

A) 0.9738
B) 0.4738
C) 0.0262
D) 0.6103
E) 0.1103

Question 34

Suppose a population has a mean of 400 and a standard deviation of 24. If a random sample of size 144 is drawn from the population, the probability of drawing a sample with a mean less than 402 is ___.

A) 0.3413
B) 0.6826
C) 0.8413
D) 0.1587
E) 0.9875

Question 35

Suppose a population has a mean of 870 and a variance of 8,100. If a random sample of size 36 is drawn from the population, the probability that the sample mean is between 840 and 900 is ___.

A) 0.9544
B) 0.6826
C) 0.8185
D) 0.5899
E) 0.0897

Question 36

Suppose the population of all colleges shows the annual parking fee per student is $110 with a standard deviation of $18. If a random sample of size 49 is drawn from the population, the probability of drawing a sample with a sample mean between $112 and $115 is ___.

A) 0.9738
B) 0.7777
C) 0.7823
D) 0.1915
E) 1.7561

Question 37

Suppose the population of all colleges shows the annual parking fee per student is $110 with a standard deviation of $18. If a random sample of size 49 is drawn from the population, the probability of drawing a sample with a sample mean between $100 and $115 is ___.

A) 0.9738
B) 0.4738
C) 0.0262
D) 0.6103
E) 0.1103

Question 38

Albert Abbasi, VP of Operations at Ingleside International Bank, is evaluating the service level provided to walk-in customers. Accordingly, he plans a sample of waiting times for walk-in customers. If the population of waiting times has a mean of 15 minutes and a standard deviation of 4 minutes, the probability that Albert's sample of 64 will have a mean less than 15 minutes is ___.

A) 0.5000
B) 0.0228
C) 0.9072
D) 0.9544
E) 1.0000

Question 39

Albert Abbasi, VP of Operations at Ingleside International Bank, is evaluating the service level provided to walk-in customers. Accordingly, he plans a sample of waiting times for walk-in customers. If the population of waiting times has a mean of 15 minutes and a standard deviation of 4 minutes, the probability that Albert's sample of 64 will have a mean less than 16 minutes is ___.

A) 0.4772
B) 0.0228
C) 0.9072
D) 0.9544
E) 0.9772

Question 40

According to the central limit theorem, for samples of size 169 drawn from a population with $\mu$ = 1,014 and $\sigma$ = 65, the standard deviation of the sampling distribution of sample means would equal ___.

A) 1,014
B) 65
C) 15
D) 6
E) 5

Question 41

Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system. If 10% of the 5,000 payroll vouchers issued since January 1, 2000, have irregularities, the probability that Pinky's random sample of 200 vouchers will have a sample proportion of between.06 and.14 is ___.

A) 0.4706
B) 0.9706
C) 0.0588
D) 0.9412
E) 0.8765

Question 42

If the population proportion is 0.90 and a sample of size 64 is taken, what is the probability that the sample proportion is more than 0.89?

A) 0.1064
B) 0.2700
C) 0.3936
D) 0.6064
E) 0.9000

Question 43

Suppose 40% of the population of pre-teens have a TV in their bedroom. If a random sample of 500 pre-teens is drawn from the population, then the probability that between 36% and 44% of the pre-teens have a TV in their bedroom is ___.

A) 0.9644
B) 0.4644
C) 0.0356
D) 0.9328
E) 0.0712

Question 44

If the population proportion is 0.90 and a sample of size 64 is taken, what is the probability that the sample proportion is less than 0.88?

A) 0.2019
B) 0.2981
C) 0.5300
D) 0.7019
E) 0.7899

Question 45

Assuming an equal chance of a new baby being a boy or a girl (that is, π = 0.5), we would like to find the probability of 40 or more of the next 100 births at a local hospital will be boys. Using the normal approximation for binomial with a correction for continuity, we should use the z score ___.

A) 0.4
B) -2.1
C) 0.6
D) 2
E) -1.7

Question 46

Suppose 40% of the population of pre-teens have a TV in their bedroom. If a random sample of 500 pre-teens is drawn from the population, then the probability that 44% or fewer of the pre-teens have a TV in their bedroom is ___.

A) 0.9644
B) 0.4644
C) 0.0356
D) 0.0400
E) 0.9600

Question 47

The probability that a call to an emergency help line is answered in less than 10 seconds is 0.8. Assume that the calls are independent of each other. Using the normal approximation for binomial with a correction for continuity, the probability that at least 75 of 100 calls are answered within 10 seconds is approximately ___.

A) 0.8
B) 0.1313
C) 0.5235
D) 0.9154
E) 0.8687

Question 48

Suppose 65% of all college students have a laptop computer at home and a sample of 150 students is taken. The mean of the sampling distribution of is

A) 0.65.
B) 6.5.
C) 97.5.
D) 0.975.
E) 15.0.

Question 49

Catherine Chao, Director of Marketing Research, needs a sample of Kansas City households to participate in the testing of a new toothpaste package. If 40% of the households in Kansas City prefer the new package, the probability that Catherine's random sample of 300 households will have a sample proportion greater than 0.45 is ___.

A) 0.9232
B) 0.0768
C) 0.4616
D) 0.0384
E) 0.8974

Question 50

Certain transportation company has a fleet of 210 vehicles. The average age of the vehicles is 4.25 years, with a standard deviation of 18 months. In a random sample of 40 vehicles, what is the probability that the average age of vehicles in the sample will be less than 4 years?

A) 0.146
B) 0.163
C) 0.180
D) 0.197
E) 0.214

Question 51

In an instant lottery, your chance of winning is 0.1. If you play the lottery 100 times and outcomes are independent, the probability that you win at least 15 percent of the time is

A) 0.4933.
B) 0.5.
C) 0.15.
D) 0.0478.
E) 0.9213.

Question 52

Suppose 40% of the population of pre-teens have a TV in their bedroom. If a random sample of 500 pre-teens is drawn from the population, then the probability that 44% or more of the pre-teens have a TV in their bedroom is ___.

A) 0.9644
B) 0.4644
C) 0.0356
D) 0.0400
E) 0.9600

Question 53

Suppose 40% of all college students have a computer at home and a sample of 64 is taken. What is the probability that more than 30 of those in the sample have a computer at home?

A) 0.3686
B) 0.1314
C) 0.8686
D) 0.6314
E) 0.1343

Question 54

Suppose 30% of the population has green eyes. If a random sample of size 1200 is drawn, then the probability that less than 348 U.S. citizens have green eyes is ___.

A) 0.2236
B) 0.2764
C) 0.2900
D) 0.7764
E) 0.3336

Question 55

Let x be a binomial random variable with n =50 and π =.3. If we use the normal distribution to approximate probabilities for this, a correction for continuity should be made. To find the probability of more than 15 successes, we should find ___.

A) P(x>15.5)
B) P(x>15)
C) P(x>14.5)
D) P(x≤14.5)
E) P(x < 15)

Question 56

The employees in certain division of Cybertronics Inc. need to complete a certification online. On average, it takes 20 hours to complete the coursework and successfully pass all tests, and the standard deviation is 6 hours. If you select a random sample of size 30, the probability that the employees in your sample have taken, on average, more than 20.5 hours is ___.

A) 0.47
B) 0.45
C) 0.41
D) 0.32
E) 0.01

Question 57

Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system. If 10% of the 5,000 payroll vouchers issued since January 1, 2000, have irregularities, the probability that Pinky's random sample of 200 vouchers will have a sample proportion greater than.06 is ___.

A) 0.4706
B) 0.9706
C) 0.0588
D) 0.9412
E) 0.9876

Question 58

Suppose 40% of all college students have a computer at home and a sample of 100 is taken. What is the probability that more than 50 of those in the sample have a computer at home?

A) 0.4793
B) 0.9793
C) 0.0207
D) 0.5207
E) 0.6754

Question 59

Catherine Chao, Director of Marketing Research, needs a sample of Kansas City households to participate in the testing of a new toothpaste package. If 40% of the households in Kansas City prefer the new package, the probability that Catherine's random sample of 300 households will have a sample proportion between 0.35 and 0.45 is ___.

A) 0.9232
B) 0.0768
C) 0.4616
D) 0.0384
E) 0.8976

Question 60

Let x be a binomial random variable with n = 35 and π =.20. If we use the normal distribution to approximate probabilities for this, we would use a mean of ___.

A) 35
B) 20
C) 70
D) 7
E) 3.5

Question 61

Suppose 65% of all college students have a laptop computer at home and a sample of 150 is taken. The standard deviation of the sampling distribution of is

A) 0.0015.
B) 0.0389.
C) 0.6500.
D) 0.4769.
E) 0.0477.

Question 62

A population has a mean age of 45 years with a standard deviation of 3 years. If a random sample of 64 is drawn from this population, what is the probability that the sample mean is greater than 45.3 years?

Question 63

In Norway, approximately 22% of vehicles are electric vehicles. What is the probability of randomly selecting 250 cars and finding out that 60 or more are electric?

A) 0.233
B) 0.223
C) 0.213
D) 0.203
E) 0.193

Question 64

Let x be a binomial random variable with n = 50 and ? = 0.3. Determine the probability of at most 13 successes, using the normal approximation for binomial distribution.

Question 65

It is known that 30% of XYZ Corporation's 25,000 employees are millionaires. If a random sample of 100 XYZ's employees is selected, what proportion of the sample will have more than 36% millionaires?