Deck 8: Sampling Distributions

Question 1

The average score of all golfers for a particular course has a mean of 75 and a standard deviation of 4.5.Suppose 81 golfers played the course today. Find the probability that the average score of the 81 golfersexceeded 76.

A) 0.0228
B) 0.1293
C) 0.4772
D) 0.3707

Answer 1

A

Question 2

The sampling distribution of the sample mean is shown. If the sample size is n = 16, what is the standarddeviation of the population from which the sample was drawn? Round to the nearest thousandth whereappropriate.

Answer 2

A

Question 3

$\mu = 54 , \sigma = 32 , n = 64$

A) $\mu \frac { \ } { x } = 54 , \sigma \frac { } { x } = 4$
B) $\mu _{\bar { x }} = 54 , \sigma_{ \bar { x } }= 32$
C) $\mu _{\bar { x }} = 54 , \sigma _{\bar { x }} = 0.5$
D) $\mu _{\bar { x }}= 6.75 , \sigma _{\bar { x }}= 4$

Answer 3

$\mu \frac { \ } { x } = 54 , \sigma \frac { } { x } = 4$

Question 4

What are the values of $\mu _{\bar { x }} \text { and } \sigma _{\bar { x }}$
for the sampling distribution of the sample mean shown?

A) $\mu _{\bar { x }} = 8 , \sigma _{\bar { x }} = 0.04$

B) $\mu _{\bar { x }} = 8 , \sigma _{\bar { x }} = 0.12$
C) $\mu _{\bar { x }} = 0.04 , \sigma _{\bar { x }}= 8$

D) $\mu _{\bar { x }}= 8 , \sigma _{\bar { x }} = 0.08$

Question 5

What are the values of $\mu _{\bar { x }} \text { and } \sigma _{\bar { x }}$
for the sampling distribution of the sample mean shown?

A) $\mu _{\bar { x }} = 390 , \sigma _{\bar { x }} = 40$

B) $\mu _{\bar { x }} = 390 , \sigma _{\bar { x }} = 120$

C) $\mu _{\bar { x }}= 40 , \sigma _{\bar { x }} = 390$

D) $\mu _{\bar { x }} = 390 , \sigma _{\bar { x }}= 80$

Question 6

2 Describe the distribution of the sample mean: nonnormal population.

Question 7

According to the law of large numbers, as more observations are added to the sample, the difference betweenthe sample mean and the population mean

A) Tends to become smaller
B) Tends to become larger
C) Remains about the same
D) Is inversely affected by the data added

Question 8

A farmer was interested in determining how many grasshoppers were in his field. He knows that thedistribution of grasshoppers may not be normally distributed in his field due to growing conditions. As hedrives his tractor down each row he counts how many grasshoppers he sees flying away. After several rows hefigures the mean number of flights to be 57 with a standard deviation of 12. What is the probability of thefarmer will count 60 or more flights on average in the next 40 rows down which he drives his tractor?

A) 0.0571
B) 0.4429
C) 0.9429
D) 0.5710

Question 9

The amount of corn chips dispensed into a 16-ounce bag by the dispensing machine has been identified aspossessing a normal distribution with a mean of 16.5 ounces and a standard deviation of 0.2 ounce. Suppose100 bags of chips were randomly selected from this dispensing machine. Find the probability that the samplemean weight of these 100 bags exceeded 16.6 ounces.

A) approximately 0
B) 0.1915
C) 0.3085
D) 0.6915

Question 10

$$\mu = 28 , \sigma = 8 , \mathrm { n } = 22$$

A)
$\mu _{\bar { x }}= 28 , \sigma _{\bar { x }} = 1.706$
B)
$\mu _{\bar { x }} = 28 , \sigma _{\bar { x }}= 0.364$


C)
$\mu _{\bar { x }} = 28 , \sigma _{\bar { x }} = 8$


D)
$\mu _{\bar { x }}= 16.166 , \sigma _{\bar { x }}= 1.706$

Provide an appropriate response.

Question 11

Furnace repair bills are normally distributed with a mean of 267 dollars and a standard deviation of 20 dollars.If 64 of these repair bills are randomly selected, find the probability that they have a mean cost between 267dollars and 269 dollars.

A) 0.2881
B) 0.7881
C) 0.2119
D) 0.5517

Question 12

The amount of money collected by a snack bar at a large university has been recorded daily for the past fiveyears. Records indicate that the mean daily amount collected is $4000 and the standard deviation is $450. Thedistribution is skewed to the right due to several high volume days (including football game days). Supposethat 100 days were randomly selected from the five years and the average amount collected from those dayswas recorded. Which of the following describes the sampling distribution of the sample mean?

A) normally distributed with a mean of $4000 and a standard deviation of $45
B) normally distributed with a mean of $4000 and a standard deviation of $450
C) normally distributed with a mean of $400 and a standard deviation of $45
D) skewed to the right with a mean of $4000 and a standard deviation of $450

Question 13

Assume that the heights of men are normally distributed with a mean of 70.7 inches and a standard deviationof 2.8 inches. If 64 men are randomly selected, find the probability that they have a mean height greater than71.7 inches.

A) 0.0021
B) 0.0210
C) 0.9005
D) 0.9979

Question 14

One year, professional sports players salaries averaged $1.9 million with a standard deviation of $0.7 million.Suppose a sample of 100 major league players was taken. Find the approximate probability that the averagesalary of the 100 players exceeded $1.1 million.

A) approximately 1
B) approximately 0
C) 0.2357
D) 0.7357

Question 15

The number of violent crimes committed in a day possesses a distribution with a mean of 2.2 crimes per dayand a standard deviation of 6 crimes per day. A random sample of 100 days was observed, and the meannumber of crimes for the sample was calculated. Describe the sampling distribution of the sample mean.

A) approximately normal with mean = 2.2 and standard deviation = 0.6
B) approximately normal with mean = 2.2 and standard deviation = 6
C) shape unknown with mean = 2.2 and standard deviation = 6
D) shape unknown with mean = 2.2 and standard deviation = 0.6

Question 16

Assume that blood pressure readings are normally distributed with a mean of 122 and a standard deviation of6.4. If 64 people are randomly selected, find the probability that their mean blood pressure will be less than 124.

A) 0.9938
B) 0.0062
C) 0.9998
D) 0.8615

Question 17

A random sample of size n is to be drawn from a population with μ= 600 and σ = 300. What size samplewould be necessary in order to ensure a standard error of 20?

Question 18

Suppose a population has a mean of 7 for some characteristic of interest and a standard deviation of 9.6. Asample is drawn from this population of size 64. What is the standard error of the mean?

A) 1.2
B) 0.7
C) 0.15
D) 3.3

Question 19

Suppose a population has a mean weight of 180 pounds and a standard deviation of 25 pounds. A sample of100 items is drawn from this population. What is the standard error of the mean?

A) 2.5
B) 1.8
C) 18.0
D) 0.25

Question 20

The sampling distribution of the sample mean is shown. If the sample size is n = 36, what is the standarddeviation of the population from which the sample was drawn? Round to the nearest thousandth whereappropriate.

Question 21

The ages of five randomly chosen cars in a parking garage are determined to be 7, 9, 3, 4, and 6 years old. If weconsider this sample of 5 in groups of 3, what is the probability of the population mean falling between 5.5 and6.5 years?

A) 0.5
B) 0.4
C) 0.55
D) 0.6

Question 22

The amount of time it takes a student to walk from her home to class has a skewed right distribution with amean of 17 minutes and a standard deviation of 2.2 minutes. If data were collected from 50 randomly selectedwalks, describe the sampling distribution of the sample mean time.8.2 Distribution of the Sample Proportion1 Describe the sampling distribution of a sample proportion.

Question 23

The owner of a computer repair shop has determined that their daily revenue has mean $7200 and standarddeviation $1200. The daily revenue totals for the next 30 days will be monitored. What is the probability thatthe mean daily revenue for the next 30 days will exceed $7000?

A) 0.1814
B) 0.8186
C) 0.5675
D) 0.4325

Question 24

Provide an appropriate response.

Question 25

The owner of a computer repair shop has determined that their daily revenue has mean $7200 and standarddeviation $1200. The daily revenue totals for the next 30 days will be monitored. What is the probability thatthe mean daily revenue for the next 30 days will be between $7000 and $7500?

A) 0.7333
B) 0.2667
C) 0.9147
D) 0.8186

Question 26

A farmer was interest in determining how many grasshoppers were in his field. He knows that the distributionof grasshoppers may not be normally distributed in his field due to growing conditions. As he drives histractor down each row he counts how many grasshoppers he sees flying away. After several rows he figuresthe mean number of flights to be 57 with a standard deviation of 12. What is the probability of the farmer willcount 52 or fewer flights on average in the next 40 rows down which he drives his tractor?

A) 0.0041
B) 0.4959
C) 0.9959
D) 0.0410

Question 27

John has six bills of paper money in the following denominations: $1, $5, $10, $20, $50, and $100 If he selects 3bills at a time how many, how many groups can be formed?

A) 20
B) 10
C) 30
D) 15

Question 28

Professor Whata Guy surveyed a random sample of 420 statistics students. One of the questions was ʺWill youtake another mathematics class?ʺ The results showed that 252 of the students said yes. What is the sample^proportion, p of students who say they will take another math class?

A) 0.6
B) 0.42
C) 0.252
D) 0.775

Question 29

To assess attitudes towards issues that affect the residents of a village, the village randomly chose 800 familiesto participate in a survey of life attitudes. The village received 628 completed surveys. What is the sampleproportion of completed surveys?

A) 0.785
B) 0.628
C) 1.274
D) 0.886

Question 30

John has six bills of paper money in the following denominations: $1, $5, $10, $20, $50, and $100 If he selects 3bills at a time what is the probability of selecting a group that has an average value of equal to or less than $25?

A) 0.45
B) 0.86
C) 0.50
D) 0.35

Question 31

A greenhouse in a tri-county area has kept track of its customers for the last several years and has determinedthat it has about 10,000 regular customers. Of those customers, 28% of them plant a vegetable garden in thespring. The greenhouse obtains a random sample of 800 of its customers. Is it safe to assume that the sampling^distribution of p, the sample proportion of customers that plant a vegetable garden, is approximately normal?

Question 32

A farmer was interested in determining how many grasshoppers were in his field. He knows that thedistribution of grasshoppers may not be normally distributed in his field due to growing conditions. As hedrives his tractor down each row he counts how many grasshoppers he sees flying away. After several rows hefigures the mean number of flights to be 57 with a standard deviation of 12. What is the probability of thefarmer will count 52 or fewer flights or 60 or more flights on average in the next 40 rows down which he driveshis tractor?

A) 0.0612
B) 0.4959
C) 0.9388
D) 0.0530

Question 33

The ages of five randomly chosen cars in a parking garage are determined to be 7, 9, 3, 4, and 6 years old. If weconsider this sample of 5 in groups of 3, what is the probability of the population mean being more than 6years?

A) 0.4
B) 0.5
C) 0.1
D) 0.6

Question 34

A national caterer determined that 87% of the people who sampled their food said that it was delicious. Arandom sample of 144 people is obtained from a population of 5000. The 144 people are asked to sample the^catererʹs food. Will the distribution of p, the sample proportion saying that the food is delicious, beapproximately normal?

Question 35

John has six bills of paper money in the following denominations: $1, $5, $10, $20, $50, and $100 If he selects 3bills at a time what is the probability of selecting a group that has an average value of at least $26?

A) 0.55
B) 0.50
C) 0.60
D) 0.45

Question 36

John has six bills of paper money in the following denominations: $1, $5, $10, $20, $50, and $100 If he selects 3bills at a time what is the probability of selecting a group that has an average value of between $40 and $45?

A) 0.15
B) 0.05
C) 0.25
D) 0.20

Question 37

A national caterer determined that 87% of the people who sampled their food said that it was delicious. Arandom sample of 144 people is obtained from a population of 5000. The 144 people are asked to sample the^catererʹs food. If p is the sample proportion saying that the food is delicious, what is the mean of the sampling^distribution of p?

A) 0.87
B) 1.25
C) 0.19
D) 0.42

Question 38

The ages of five randomly chosen cars in a parking garage are determined to be 7, 9, 3, 4, and 6 years old. If weconsider this sample of 5 in groups of 3, how many groups can be formed?

A) 10
B) 5
C) 30
D) 60

Question 39

The owner of a computer repair shop has determined that their daily revenue has mean $7200 and standarddeviation $1200. The daily revenue totals for the next 30 days will be monitored. What is the probability thatthe mean daily revenue for the next 30 days will exceed $7500?

A) 0.0853
B) 0.9131
C) 0.0869
D) 0.9147

Question 40

A national caterer determined that 37% of the people who sampled their food said that it was delicious. Arandom sample of 144 people is obtained from a population of 5000. The 144 people are asked to sample the^catererʹs food. If p is the sample proportion saying that the food is delicious, what is the standard deviation of^the sampling distribution of p?

A) 0.04
B) 0.002
C) 0.48
D) 0.23

Question 41

If a population proportion is believed to be 0.6, how many items must be sampled to ensure that the sampling^distribution of p will be approximately normal? Assume that the size of the population is N = 10,000.

A) 42
B) 30
C) 13
D) 60

Question 42

The National Association of Realtors estimates that 23% of all homes purchased in 2004 were consideredinvestment properties. If a sample of 800 homes sold in 2004 is obtained and it was noted that 248 homes wereto be used as investment property, would this be unusual?

Question 43

The National Association of Realtors estimates that 23% of all homes purchased in 2004 were consideredinvestment properties. If a sample of 800 homes sold in 2004 is obtained what is the probability that at least 175homes are going to be used as investment property?

A) 0.7764
B) 0.4821
C) 0.2236
D) 0.5189

Question 44

2 Compute probabilities of a sample proportion.

Question 45

Smith is a weld inspector at a shipyard. He knows from keeping track of good and substandard welds that forthe afternoon shift 5% of all welds done will be substandard. If Smith checks 300 of the 7500 welds completedthat shift, what is the probability that he will find less than 20 substandard welds?

A) 0.9066
B) 0.4066
C) 0.0934
D) 0.5934

Question 46

Smith is a weld inspector at a shipyard. He knows from keeping track of good and substandard welds that forthe afternoon shift 5% of all welds done will be substandard. If Smith checks 300 of the 7500 welds completedthat shift, what is the probability that he will find more than 25 substandard welds?

A) 0.0040
B) 0.4960
C) 0.5040
D) 0.9960

Question 47

Smith is a weld inspector at a shipyard. He knows from keeping track of good and substandard welds that forthe afternoon shift 5% of all welds done will be substandard. If Smith checks 300 of the 7500 welds completedthat shift, would it be unusual for Smith to find 30 or more substandard welds?

A) Yes
B) No

Question 48

The National Association of Realtors estimates that 23% of all homes purchased in 2004 were consideredinvestment properties. If a sample of 800 homes sold in 2004 is obtained what is the probability that at most200 homes are going to be used as investment property?

A) 0.9099
B) 0.4066
C) 0.0934
D) 0.5935

Question 49

A simple random sample of size n=1320 is obtained from a population whose size is N=1,400,000 and whose population proportion with a specified characteristic is p=0.46 . Describe the sampling distribution of https://d2lvgg3v3hfg70.cloudfront.net/TB34225555/.

A) Approximately normal;
B) Exactly normal;
C) Approximately normal;
D) Exactly normal;

Question 50

The National Association of Realtors estimates that 23% of all homes purchased in 2004 were consideredinvestment properties. If a sample of 800 homes sold in 2004 is obtained what is the probability that between175 and 200 homes are going to be used as investment property?

A) 0.1335
B) 0.9099
C) 0.7764
D) 0.2236

Question 51

Smith is a weld inspector at a shipyard. He knows from keeping track of good and substandard welds that forthe afternoon shift 5% of all welds done will be substandard. If Smith checks 300 of the 7500 welds completedthat shift, what is the probability that he will find between 10 and 20 substandard welds?

A) 0.8132
B) 0.4066
C) 0.2033
D) 0.6377

Question 52

A greenhouse in a tri-county area has kept track of its customers for the last several years and has determinedthat 28% of its customers plant a vegetable garden in the spring. The greenhouse obtains a random sample of^1000 of its customers. What is the mean of the sampling distribution of p, the sample proportion of customersthat plant a vegetable garden in the spring?

A) 0.28
B) 0.72
C) 2800
D) 0.002