Deck 8: Sampling Distributions

Question 1

The average number of customers that visited a particular store during the past year is 160 per day and a standard deviation of 25 customers per day.A random sample of 64 days is chosen from this population.The standard deviation of the sample mean equals:

A) 12.649.
B) 25.0.
C) 2.56.
D) 3.125.
E) 8.0

Answer 1

3.125.

Question 2

Each of the following are characteristics of the sampling distribution of the mean except:

A) The sampling distribution of the mean has the same mean as the original population.
B) The standard deviation of the sampling distribution of the mean is referred to as the standard error.
C) If the original population is normally distributed,the sampling distribution of the mean will also be normal.
D) If the original population is not normally distributed,the sampling distribution of the mean will also be approximately normal for large sample sizes.
E) All of the above are characteristics of the sampling distribution of the mean.

Answer 2

All of the above are characteristics of the sampling distribution of the mean.

Question 3

A manufacturing company packages peanuts for Piedmont Airlines.The individual packages weigh 1.4 grams with a standard deviation of 0.6 grams.For a flight of 152 passengers receiving the peanuts,the probability that the average weight of the packages is less than 1.3 grams is:

A) 0.0202.
B) 0.2040.
C) 0.9798.
D) 0.4798.
E) 2.0500.

Answer 3

0.0202.

Question 4

The sampling distribution of the mean will be normal if the original population from which the samples were drawn is normally distributed.

Question 5

The standard error for the sampling distribution of the mean is equal to $\frac { \sigma } { \sqrt { n } }$ .

Question 6

If all possible samples of size n are drawn from an infinite population with a mean of $\mu$ and a standard deviation of $\text { ? }$
,then the standard error of the sample mean is inversely proportional to:

A) ?
B) $\sqrt { \mathrm { n } }$
C) ?
D) n.

Question 7

The average sales per customer at a home improvement store during the past year is $75 with a standard deviation of $12.The probability that the average sales per customer from a sample of 36 customers,taken at random from this population,exceeds $78 is:

A) 0.4332.
B) 0.0668.
C) 0.0987.
D) 0.9013.
E) 0.5000

Question 8

When a great many simple random samples are drawn from a population that is normally distributed,the same means will also be normally distributed only when the sample size is greater than 30.

Question 9

In a given year,the average annual salary of a NFL football player was $189,000 with a standard deviation of $20,500.If a sample of 50 players was taken,then probability that the sample mean will be $192,000 or more is:

A) 0.6970.
B) 0.3485.
C) 0.1515.
D) 0.0398.
E) 0.4602.

Question 10

The sampling distribution of the mean will have the same standard deviation as the original population from which the samples were drawn.

Question 11

The concept that allows us to draw conclusions about the population based strictly on sample data without having any knowledge about the distribution of the underlying population is

A) the central limit theorem.
B) the standard error of the mean.
C) the normal distribution.
D) the standard deviation.
E) the variance.

Question 12

The standard error is:

A) the standard deviation of the sampling distribution.
B) the squared value of the population variance.
C) the same value as the population standard deviation.
D) is the same for distributions of all sample sizes.
E) is the mean of the sampling distribution

Question 13

The sample proportion can be considered a random variable that will take on different values as the procedure leading to the sample proportion is repeated a great many times.

Question 14

The sampling distribution of the mean will be approximately normal regardless of the distribution of the original population or the sample size.

Question 15

The number of all possible simple random samples of size 2 that can be taken from a population of 5 elements is 6.

Question 16

Sample data are used as the basis from which to make probability statements about the true (but unknown)value of the population mean or proportion.

Question 17

The Central Limit Theorem states that the sampling distribution of the mean will be approximately normal provided that the sample size is greater than 30.

Question 18

The average speed of cars passing a checkpoint is 60 miles per hour with a standard deviation of 8 miles per hour.Fifty (50)passing cars are clocked at random from this checkpoint.The probability that the sample mean will be between 57 and 62 miles per hour is:

A) 0.9576.
B) 0.9960.
C) 0.2467.
D) 0.3520.
E) 0.4659

Question 19

The sampling distribution of the mean will have the same mean as the original population from which the samples were drawn.

Question 20

If a population is a Poisson distribution with a mean of 4,then the sampling distribution of the mean for 200 Excel or Minitab simulated samples approaches the normal distribution as the sample sizes are 5 or more.

Question 21

The average weight of a 4 year old male is 40 lbs with a standard deviation of 6 lbs.What would be the probability that the average weight from a random sample of 50 boys at this age would have be greater than 41 lbs?

Question 22

Fifty percent of all college students attend schools within 50 miles of their homes.In a sample of 500 college students,the probability that the sample proportion will be between 0.45 and 0.55 is:

A) 0.4875.
B) 0.9818.
C) 0.4909.
D) 0.9750.
E) 0.5000.

Question 23

As a general rule,the normal distribution is used to approximate the sampling distribution of the sample proportion only if:

A) the sample size n is greater than or equal to 30.
B) the population proportionis close to 0.50.
C) the underlying population is normal.
D) nand nare both greater than or equal to 5.

Question 24

The Coca-Cola Company has 40% of the cola market.Determine the probability that a sample proportion for n = 30 is within 0.10 of the true proportion of 0.40,which is the proportion of cola drinkers who prefer a Coca-Cola drink.In this particular market,the population size of those who drink cola is 50.

A) 0.7372
B) 0.3686
C) 0.4599
D) 0.9198
E) Not enough information given to make calculation.

Question 25

A manufacturer of galvanized chains advertises the load capacity of a 16-foot length of chain has an average of 2650 lbs.and a standard deviation of 520 lbs.If a retailer receives an order of 75 chains,what is the probability that the sample mean will be greater than 2775 lbs?

Question 26

Your company is located in New York City and your job requires that you travel by air to many other major cities such as Boston,Chicago,Los Angeles,Detroit,Houston,Dallas,Atlanta,Denver,and Washington,DC.Your average round-trip airfare for the past year has been $495 with a standard deviation of $240.If for your next year's planning budget you estimate your average air ticket between $395 and $550,what is the probability that the mean, ,of your next 36 flights will fall in this range?

Question 27

The average cost of renting a compact size car in a major metropolitan area of the U.S.is $51.74 with a standard deviation of $7.48.Assume a normal distribution.If a sample of 20 cities is taken,what is the probability that the sample mean will fall between 47.74 and 55.74?

Question 28

Fifty percent of all college students attend schools within 50 miles of their homes.In a sample of 500 college students from a city with 5000 college students,what is the probability that the sample proportion will be between 0.45 and 0.55?

A) 0.4875
B) 0.9818
C) 0.4909
D) 0.9750
E) 0.5000

Question 29

In a simple random sample of 1,000 automobile owners between ages 25-35,there were 142 owners of a Ford Explorer.If the expected number of owners of this vehicle was 125 out of 1000,the values of $\pi$
p,and n are,respectively:

A) 125,142,1000.
B) 142,125,1000.
C) 0.142,0.125,1000.
D) 0.125,0.142,1000.
E) 0.142,0.125,1350.

Question 30

A normally distributed population with 200 elements has a mean of 60 and a standard deviation of 10.The probability that the mean of a sample of 25 elements taken from this population will be smaller than 56 is:

A) 0.0166.
B) 0.0228.
C) 0.3708.
D) 0.0394.

Question 31

Historically,a company that mails its monthly catalog to potential customers receives orders from 8 percent of the addresses.If 500 addresses are selected randomly from the last mailing,what is the probability that between 35 and 50 orders were received from this sample?

A) 0.0496
B) 0.2049
C) 0.7444
D) 0.7951
E) 0.9504

Question 32

Sixty percent of a company's customers are females.What is the probability that a random sample of 200 customers is greater than 64 percent female?

A) 0.1229
B) 0.1556
C) 0.1898
D) .02158
E) 0.2847

Question 33

A manufacturer of printers claims that their color cartridge will print an average of 200 4-by-6 photos with a standard deviation of 60 photos.A random sample of 40 customers counted the number of photos printed with one cartridge.If the manufacturer's claim is correct,what is the probability that the average customer printed at least 210 pages with one cartridge?

Question 34

A population that consists of 500 observations has a mean of 40 and a standard deviation of 15.A sample of size 100 is taken at random from this population.The standard error of the sample mean equals:

A) 2.50.
B) 12.50.
C) 1.343.
D) 1.50.

Question 35

Suppose an actual census showed that 18.4% of the households in California have incomes in excess of $50,000.What is the probability that the sample proportion will be 0.22 or greater for a random sample of 750 households from a city population which totals 10,000?

A) 0.0055
B) 0.9945
C) 0.9949
D) 0.0041
E) Not enough information given for estimation.

Question 36

The Coca-Cola Company has 40% of the cola market.The probability that a sample proportion for n = 30 falls within 0.10 of the true population proportion of 0.40,which represents the proportion of cola drinkers who prefer a Coca-Cola drink is:

A) 0.7372.
B) 0.3686.
C) 0.4599.
D) 0.9198.
E) not enough information given to make calculation.

Question 37

Suppose an actual census showed that 18.4% of the households in California have incomes in excess of $50,000.The probability that the sample proportion will be 0.22 or greater for a random sample of 750 households is:

A) 0.0055.
B) 0.9945.
C) 0.9949.
D) 0.0041.
E) not enough information given for estimation.

Question 38

An airline,in response to passenger concern,conducts realistic tests to determine the time needed to evacuate a Boeing 737.Average evacuation time in the past has been 100 seconds with a standard deviation of 15 seconds.The FFA requires tests that show a planeload of passengers can be evacuated in 92 seconds.If the airline conducts a sample of 30 tests,what is the probability that the average evacuation time will be ninety-two seconds or less?

Question 39

An auditor knows from past history that the average accounts receivable for ABC Company is $441.27 with a standard deviation of $555.48.If the auditor takes a sample of 100 accounts,what is the probability that the mean of the sample will be within $100 of the population mean?

Question 40

A sample of size n is selected at random from an infinite population.As n increases,which of the following statements is true?

A) The population standard deviation decreases
B) The standard error of the sample mean decreases
C) The population standard deviation increases
D) The standard error of the sample mean increases
E) The sample mean increases.

Question 41

The probability of a success on any trial of a binomial experiment is 20%.Find the probability that the proportion of success in a sample of 400 is less than 18%.

Question 42

A trucking firm has trucks that average a payload of 22.5 tons and a standard deviation of 1.5 tons.An accounting firm is auditing the shipping orders for the past year for billing errors.It chooses a random sample of 64 shipping orders.What is the probability that the sample mean weight will be within 1 ton of the true population mean of 22.5 tons?

Question 43

In a production of 1000 plastic moldings,75 were incompletely formed and had to be discarded.Based on these data the total production of plastic moldings should have what estimated proportion of incompletely formed moldings?

Question 44

A population consisted of 500 cases involving shoplifters.If a random sample of 300 was taken and in 90 cases the offender was under age 18,in how many of the 500 cases would you say the person involved was under age 18?
____________________ cases

Question 45

The chairman of a statistics department in a certain college believes that 70% of the department's graduate assistantships are given to international students.A random sample of 50 graduate assistants is taken.Assume that the chairman is correct and that = 0.70.What is the probability that the sample proportion p will be between 0.65 and 0.73?

Question 46

The amount of time spent by American adults playing sports per day is normally distributed with a mean of 4 hours and standard deviation of 1.25 hours.Find the probability that a randomly selected American adult plays sports for more than 5 hours per day.

Question 47

A producer of a juice drink advertises that it contains 10% real fruit juices.A sample of 75 bottles of the drink is analyzed and the percent of real fruit juices is found to be 6.5%.If the true proportion is actually 0.10,what is the probability that the sample percent will be 6.5% or less?

Question 48

In an effort to identify the true proportion of shoplifters who are under age 18,a random sample of 300 shoplifting cases was taken.One hundred and twenty of those cases involved persons under age 18.What value would be used to estimate the true proportion of under age 18 shoplifters?

Question 49

The publisher of a daily newspaper claims that 90% of its subscribers are under the age of 30.Suppose that a sample of 300 subscribers is selected at random.Assuming the claim is correct,approximate the probability of finding at least 240 subscribers in the sample under the age of 30.

Question 50

A manufacturer of printers claims that their color cartridge will print an average of 200 4-by-6 photos with a standard deviation of 60 photos.A random sample of 40 customers counted the number of photos printed with one cartridge.If the manufacturer's claim is correct,what is the probability that the average customer printed less than 195 pages with one cartridge?

Question 51

The heights of men in the USA are normally distributed with a mean of 68 inches and a standard of 4 inches.A random sample of five men is selected.What is the probability that the sample mean is greater than 70 inches?

Question 52

If young children watch an average of 105 minutes of TV per day with a standard deviation of 30 minutes per day,what is the probability that a random sample of 60 children will watch more than 110 minutes of TV per day?

Question 53

Suppose it is known that 60% of students at a particular college are smokers.A sample of 500 students from the college is selected at random.Approximate the probability that at least 280 of these students are smokers.

Question 54

The heights of men in the USA are normally distributed with a mean of 68 inches and a standard of 4 inches.What is the probability that a randomly selected man is taller than 70 inches?

Question 55

A manufacturer of printers claims that their color cartridge will print an average of 200 4-by-6 photos with a standard deviation of 60 photos.A random sample of 40 customers counted the number of photos printed with one cartridge.If the manufacturer's claim is correct,what is the probability that the average customer printed at least 185 pages with one cartridge?

Question 56

A videocassette rental store wants to know what proportion of its stock should include the Beta format VCR.A random sample of the owners of VCRs is suggested.Five hundred VCR owners are asked if they own the Beta or VHS format.Out of 500 interviewed,125 were owners of the Beta format.Presume that the true population proportion of Beta format VCRs is = 0.32.What is the probability that the sample proportion p will be within 0.04 of the true proportion of Beta format ownership?

Question 57

A manufacturer of printers claims that their color cartridge will print an average of 200 4-by-6 photos with a standard deviation of 60 photos.A random sample of 40 customers counted the number of photos printed with one cartridge.If the manufacturer's claim is correct,what is the probability that the average customer printed between 190 and 205 pages with one cartridge?

Question 58

The amount of time spent by American adults playing sports per day is normally distributed with a mean of 4 hours and standard deviation of 1.25 hours.Find the probability that if four American adults are randomly selected,their average number of hours spent playing sports is more than 5 hours per day.

Question 59

The heights of men in the USA are normally distributed with a mean of 68 inches and a standard of 4 inches.What is the probability that the mean height of a random sample of 35 men is greater than 70 inches?

Question 60

The Sunbelt City Peewee baseball organization has ordered 48 dozen balls from the Liteflite Company for use in its summer program.The company has guaranteed a 10% discount on the total cost if 32 or more of the balls are defective.Experience in the past has shown 5% defects.A sample of 50 balls will be taken,and the discount will be given if the sample proportion of defective balls is at least 32 in 48 dozen.What is the probability that the organization will get the 10% discount?

Question 61

NARRBEGIN: Vehicles
Four families live on a cul-de-sac represent a very small population.The number of vehicles owned by each family is shown below:
Calculate the population standard deviation.

Question 62

The average SAT score for the 300 students accepted at Tiny College this year is 1050 with a standard deviation of 275.If a random sample of 40 students is selected from this class,what is the probability that the average SAT score will be greater than 1070?

Question 63

NARRBEGIN: Vehicles
Four families live on a cul-de-sac represent a very small population.The number of vehicles owned by each family is shown below:
List all possible simple random samples of size two that can be taken from this population and determine the mean number of vehicles for each sample.

Question 64

NARRBEGIN: Vehicles
Four families live on a cul-de-sac represent a very small population.The number of vehicles owned by each family is shown below:
Calculate the standard deviation of the sample means.

Question 65

Assume that all possible simple random samples of size two are taken from this population,and that the original population is normally distributed.Apply the Central Limit Theorem to find the mean of the sampling distribution of sample means.

Question 66

Using information from a sample to reach conclusions about the population from which it was drawn is referred to as ____________________.

Question 67

Calculate the population mean and standard deviation.
Mean = ____________________
SD = ____________________

Question 68

The average SAT score for the 300 students accepted at Tiny College this year is 1050 with a standard deviation of 275.If a random sample of 40 students is selected from this class,what is the probability that the average SAT score will be greater than 1000?

Question 69

NARRBEGIN: Pets
Determine the probability distribution for the discrete random variable,x = number of pets owned.

Question 70

When a great many simple random samples of size n are drawn from a population that is normally distributed,the sampling distribution of the sample means will be ____________________ regardless of sample size n.As n increases,the ____________________ of the sample distribution will become smaller.

Question 71

In a selected year,the top 50 performers in men's professional tennis averaged 24.04 years of age with a standard deviation of 3.63 years.A random sample of ten is taken.Compute the standard deviation of .

Question 72

NARRBEGIN: Vehicles
Four families live on a cul-de-sac represent a very small population.The number of vehicles owned by each family is shown below:
Calculate the mean of the sample means.

Question 73

If the original population from which the samples were drawn is not normally distributed,then the sampling distribution of the mean will be ____________________ for large sample sizes.

Question 74

A Poisson probability distribution with a mean of 4 must have a standard deviation of ____________________.

Question 75

The average SAT score for the 300 students accepted at Tiny College this year is 1050 with a standard deviation of 275.If a random sample of 40 students is selected from this class,what is the probability that the average SAT score will be between 1060 and 1120?

Question 76

Assume that all possible simple random samples of size two are taken from this population,and that the original population is normally distributed.Apply the Central Limit Theorem to find the standard error of the sampling distribution of sample means.

Question 77

The chairman of a statistics department in a certain college believes that 70% of the department's graduate assistantships are given to international students.A random sample of 50 graduate assistants is taken.Assume that the chairman is correct and that = 0.70.What is the probability that the sample proportion p will be within 0.05 of the population proportion ?

Question 78

In order to estimate the mean salary for a population of 500 employees,the president of a certain company selected at random a sample of 40 employees.What is the probability that the sample mean salary of the employees will be within $200 of the population mean salary?

Question 79

The standard deviation of the sampling distribution of the mean is referred to as the ____________________.

Question 80

NARRBEGIN: Vehicles
Four families live on a cul-de-sac represent a very small population.The number of vehicles owned by each family is shown below:
Calculate the population mean.