Exam 7: Sampling Distributions

SCENARIO 7-1 The time spent studying by students in the week before final exams follows a normal distribution with a standard deviation of 8 hours.A random sample of 4 students was taken to estimate the mean study time for the population of all students. -Referring to Scenario 7-1, what is the probability that the sample mean is more than 3 hours below the population mean?

SCENARIO 7-5 According to an article, 19% of the entire population in a developing country has high-speed access to the Internet.Random samples of size 200 are selected from the country's population. -Referring to Scenario 7-5, among all the random samples of size 200, % will have between 9% and 29% who have high-speed access to the Internet.

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, the standard error of all possible sample proportions is .

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, what is the probability that the sample mean selling price was between$113,000 and $117,000?

Sampling distributions describe the distribution of

For sample size 1, the sampling distribution of the mean will be normally distributed

If the population distribution is unknown, in most cases the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 30 observations.

Which of the following statements about the sampling distribution of the sample mean isincorrect?

SCENARIO 7-3 The lifetimes of a certain brand of light bulbs are known to be normally distributed with a mean of 1,600 hours and a standard deviation of 400 hours.A random sample of 64 of these light bulbs is taken. -Referring to Scenario 7-3, what is the probability that the sample mean lifetime is more than1,550 hours?

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

SCENARIO 7-5 According to an article, 19% of the entire population in a developing country has high-speed access to the Internet.Random samples of size 200 are selected from the country's population. -Referring to Scenario 7-5, among all the random samples of size 200, % will have between 14% and 24% who have high-speed access to the Internet.

The amount of tea leaves in a can from a production line is normally distributed with $\mu = 110$ grams and $\sigma = 25$ grams.A sample of 25 cans is to be selected.What is the probability that thesample mean will be between 100 and 120 grams?

To use the normal distribution to approximate the binomial distribution, we need andto be at least 5.

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?

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound.If a sample of25 fish yields a mean of 3.6 pounds, what is the Z-score for this observation?

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound.If a sample of16 fish is taken, what would the standard error of the mean weight equal?

SCENARIO 7-5 According to an article, 19% of the entire population in a developing country has high-speed access to the Internet.Random samples of size 200 are selected from the country's population. -Referring to Scenario 7-5, among all the random samples of size 200, % will have less than 20% who have high-speed access to the Internet.

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 is the probability that a random sample of 50 will have at least30% of customers who will make a purchase after visiting the web site?

The amount of tea leaves in a can from a production line is normally distributed with $\mu = 110$ grams and $\sigma = 25$ grams.A sample of 25 cans is to be selected.What is the probability that thesample mean will be greater than 100 grams?