Exam 7: Sampling Distributions

A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes.Suppose a random sample of 64 purchasers of this table saw is taken.The probability that the sample mean will be less than 82 minutes is .

SCENARIO 7-6 Online customer service is a key element to successful online retailing.According to a marketing survey,37.5% of online customers take advantage of the online customer service.Random samples of 200 customers are selected. -Referring to Scenario 7-6,_____% of the samples are likely to have between 35% and 40% who take advantage of online customer service.

SCENARIO 7-2 The mean selling price of new homes in a small town over a year was $115,000.The population standard deviation was $25,000.A random sample of 100 new home sales from this city was taken. -Referring to Scenario 7-2,without doing the calculations,state in which of the following ranges the sample mean selling price is most likely to lie?

If the amount of gasoline purchased per car at a large service station has a population mean of 15 gallons and a population standard deviation of 4 gallons,then 99.73% of all cars will purchase between 3 and 27 gallons.

The sample proportion is an unbiased estimator for the population proportion.

The mean of the sampling distribution of a sample proportion is the population proportion, $\pi$

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes.A random sample of 16 cars is selected.90% of the sample means will be greater than what value?

A sampling distribution is defined as the probability distribution of possible sample sizes that can be observed from a given population.

Suppose the ages of students in Statistics 101 follow a right skewed distribution with a mean of 23 years and a standard deviation of 3 years.If we randomly sampled 100 students,which of the following statements about the sampling distribution of the sample mean age is incorrect ?

The amount of bleach a machine pours into bottles has a mean of 36 oz.with a standard deviation of 0.15 oz.Suppose we take a random sample of 36 bottles filled by this machine.The probability that the mean of the sample is between 35.94 and 36.06 oz.is .

Suppose a sample of n = 50 items is selected from a population of manufactured products and the weight,X,of each item is recorded.Prior experience has shown that the weight has a probability distribution with μ = 6 ounces and σ= 2.5 ounces.Which of the following is true about the sampling distribution of the sample mean if a sample of size 15 is selected?

SCENARIO 7-6 Online customer service is a key element to successful online retailing.According to a marketing survey,37.5% of online customers take advantage of the online customer service.Random samples of 200 customers are selected. -Referring to Scenario 7-6, 90% of the samples proportions symmetrically around the population proportion will have between _____% and _____% of the customers who take advantage of online customer service.

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past.Suppose a sample of 100 major league players was taken.Find the approximate probability that the mean salary of the 100 players exceeded $4.0 million.

Sampling distributions describe the distribution of

A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes.Suppose a random sample of 64 purchasers of this table saw is taken.The probability that the sample mean will be between 77 and 89 minutes is .

At a computer manufacturing company,the actual size of a computer chip is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter.A random sample of 12 computer chips is taken.What is the probability that the sample mean will be below 0.95 centimeters?

SCENARIO 7-4 According to a survey,only 15% of customers who visited the web site of a major retail store made a purchase.Random samples of size 50 are selected. -Referring to Scenario 7-4,what proportion of the samples will have less than 15% of customers who will make a purchase after visiting the web site?

A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes.Suppose a random sample of 64 purchasers of this table saw is taken.The probability that the sample mean will be greater than 88 minutes is .

SCENARIO 7-4 According to a survey,only 15% of customers who visited the web site of a major retail store made a purchase.Random samples of size 50 are selected. -Referring to Scenario 7-4,the standard deviation of all the sample proportions of customers who will make a purchase after visiting the web site is .

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past.Suppose a sample of 100 major league players was taken.Find the approximate probability that the mean salary of the 100 players was less than $2.5 million.