Question 1

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

Accepted Answer

The answer of Poker Time The amount of time spent...

Question 2

Retirees A sample of 50 retirees is drawn at random from a normal population whose mean age and standard deviation are 75 and 6 years, respectively. {Retirees Narrative} What is the probability that the mean age is at most 73 years?

Accepted Answer

The answer of Retirees A sample of 50 retirees is...

Question 3

Magazines A local magazine store sells an average of 2,100 magazines per day, with a standard deviation of 500 magazines. Consider a sample of 60 days of operation. {Magazines Narrative} Find the expected value and the standard error of the sample mean.

Accepted Answer

The answer of Magazines A local magazine store sells an...

Question 4

Retirees A sample of 50 retirees is drawn at random from a normal population whose mean age and standard deviation are 75 and 6 years, respectively. {Retirees Narrative} What is the probability that two randomly selected retirees are over 73 years of age?

Accepted Answer

The answer of Retirees A sample of 50 retirees is...

Question 5

The probability of success on any trial of a binomial experiment is 20%. Find the probability that the proportion of success in a sample of 400 is: 
 a. less than 18%. 
 b. more than 18%. 
 c. between 18% and 22%.

Accepted Answer

The answer of The probability of success on any trial...

Question 6

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

Accepted Answer

The answer of Heights of Men The heights of men...

Question 7

Magazines A local magazine store sells an average of 2,100 magazines per day, with a standard deviation of 500 magazines. Consider a sample of 60 days of operation. {Magazines Narrative} What is the shape of the sampling distribution of the sample mean number of magazines sold per day? Why?

Accepted Answer

The answer of Magazines A local magazine store sells an...

Question 8

A CPA knows from past history that the average accounts receivable for a company is $521.72 with a standard deviation of $584.64. If the auditor takes a simple random sample of 100 accounts, what is the probability that the mean of the sample is within $120 of the population mean?

Accepted Answer

The answer of A CPA knows from past history that...

Question 9

Heights of Men The heights of men in the USA are normally distributed with a mean of 68 inches and a standard deviation of 4 inches. {Heights of Men Narrative} What is the probability that the mean height of a random sample of 36 men is greater than 70 inches?

Accepted Answer

The answer of Heights of Men The heights of men...

Question 10

Magazines A local magazine store sells an average of 2,100 magazines per day, with a standard deviation of 500 magazines. Consider a sample of 60 days of operation. {Magazines Narrative} What is the probability that the sample mean is between 2,000 and 2,300 magazines?

Accepted Answer

The answer of Magazines A local magazine store sells an...

Question 11

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

Accepted Answer

The answer of Heights of Men The heights of men...

Question 12

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

Accepted Answer

The answer of Poker Time The amount of time spent...

Question 13

Number of Fish Tanks The following data give the number of fish tanks owned for a population of 4 families.  {Number of Fish Tanks Narrative} Find the sampling distribution of  , and use it to calculate the mean and the standard deviation of  .

Accepted Answer

The answer of Number of Fish Tanks The following data...

Question 14

Heights of Men The heights of men in the USA are normally distributed with a mean of 68 inches and a standard deviation of 4 inches. {Heights of Men Narrative} If the population of men's heights is not normally distributed, which, if any, of the previous questions can you answer?

Accepted Answer

The answer of Heights of Men The heights of men...

Question 15

Suppose it is known that 60% of radio listeners 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 radio listeners.

Accepted Answer

The answer of Suppose it is known that 60% of...

Question 16

Number of Fish Tanks The following data give the number of fish tanks owned for a population of 4 families.  {Number of Fish Tanks Narrative} A sample of size 2 is drawn at random from the population. Use the formulas  and  to calculate the mean and the standard deviation of the sampling distribution of the sample means.

Accepted Answer

The answer of Number of Fish Tanks The following data...

Question 17

Number of Fish Tanks The following data give the number of fish tanks owned for a population of 4 families.  {Number of Fish Tanks Narrative} List all possible samples of 2 families that can be selected without replacement from this population, and compute the sample mean  for each sample.

Accepted Answer

The answer of Number of Fish Tanks The following data...

Question 18

Number of Fish Tanks The following data give the number of fish tanks owned for a population of 4 families.  {Number of Fish Tanks Narrative} Find the mean and the standard deviation for the population.

Accepted Answer

The answer of Number of Fish Tanks The following data...

Question 19

In a given year, the average annual salary of a NHL hockey player was $205,000 with a standard deviation of $24,500. If a simple random sample of 50 players was taken, what is the probability that the sample mean will exceed $210,000?

Accepted Answer

The answer of In a given year, the average annual...

Question 20

Retirees A sample of 50 retirees is drawn at random from a normal population whose mean age and standard deviation are 75 and 6 years, respectively. {Retirees Narrative} What is the probability that the mean age exceeds 73 years?

Accepted Answer

The answer of Retirees A sample of 50 retirees is...

Quiz 8: Sampling Distributions

Retirees A sample of 50 retirees is drawn at random from a normal population whose mean age and standard deviation are 75 and 6 years, respectively. {Retirees Narrative} What is the probability that the mean age is at most 73 years?

Magazines A local magazine store sells an average of 2,100 magazines per day, with a standard deviation of 500 magazines. Consider a sample of 60 days of operation. {Magazines Narrative} Find the expected value and the standard error of the sample mean.

Retirees A sample of 50 retirees is drawn at random from a normal population whose mean age and standard deviation are 75 and 6 years, respectively. {Retirees Narrative} What is the probability that two randomly selected retirees are over 73 years of age?

The probability of success on any trial of a binomial experiment is 20%. Find the probability that the proportion of success in a sample of 400 is: a. less than 18%. b. more than 18%. c. between 18% and 22%.

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

Magazines A local magazine store sells an average of 2,100 magazines per day, with a standard deviation of 500 magazines. Consider a sample of 60 days of operation. {Magazines Narrative} What is the shape of the sampling distribution of the sample mean number of magazines sold per day? Why?

A CPA knows from past history that the average accounts receivable for a company is $521.72 with a standard deviation of $584.64. If the auditor takes a simple random sample of 100 accounts, what is the probability that the mean of the sample is within $120 of the population mean?

Heights of Men The heights of men in the USA are normally distributed with a mean of 68 inches and a standard deviation of 4 inches. {Heights of Men Narrative} What is the probability that the mean height of a random sample of 36 men is greater than 70 inches?

Magazines A local magazine store sells an average of 2,100 magazines per day, with a standard deviation of 500 magazines. Consider a sample of 60 days of operation. {Magazines Narrative} What is the probability that the sample mean is between 2,000 and 2,300 magazines?

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

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

Number of Fish Tanks The following data give the number of fish tanks owned for a population of 4 families. {Number of Fish Tanks Narrative} Find the sampling distribution of , and use it to calculate the mean and the standard deviation of .

Heights of Men The heights of men in the USA are normally distributed with a mean of 68 inches and a standard deviation of 4 inches. {Heights of Men Narrative} If the population of men's heights is not normally distributed, which, if any, of the previous questions can you answer?

Suppose it is known that 60% of radio listeners 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 radio listeners.

Number of Fish Tanks The following data give the number of fish tanks owned for a population of 4 families. {Number of Fish Tanks Narrative} List all possible samples of 2 families that can be selected without replacement from this population, and compute the sample mean for each sample.

Number of Fish Tanks The following data give the number of fish tanks owned for a population of 4 families. {Number of Fish Tanks Narrative} Find the mean and the standard deviation for the population.

In a given year, the average annual salary of a NHL hockey player was $205,000 with a standard deviation of $24,500. If a simple random sample of 50 players was taken, what is the probability that the sample mean will exceed $210,000?

Retirees A sample of 50 retirees is drawn at random from a normal population whose mean age and standard deviation are 75 and 6 years, respectively. {Retirees Narrative} What is the probability that the mean age exceeds 73 years?