Exam 10: Sampling Distributions

Suppose that the mean income of people in a region is $35,000 with a standard deviation of $6,000. It is known that the population is unimodal and symmetric. For a sample of size 25, a. Describe the sampling distribution of the sample mean. b. What is the probability of obtaining from a sample of 25 people an average income that is above $37,000?

A golf course in Toronto has determined that the mean time it takes for a foursome to complete an 18-hole round of golf is 4 hours 35 minutes (275 minutes) with a standard deviation of 14 minutes. The time distribution is also thought to be approximately Normal. Every month, the head pro at the course randomly selects a sample of 8 foursomes and monitors the time it takes them to play. Suppose the mean time that was observed for the sample last month was 4 hours 44 minutes (284 minutes). What is the probability of seeing a sample mean this high or higher?

Consider the following to answer the question(s) below: According to a recent survey, about 33% of Canadians polled said that they would likely purchase reusable cloth bags for groceries in order to reduce plastic waste. Suppose 45 shoppers are interviewed at a local supermarket. -Which of the following statements is (are) false about the sampling distribution of the sample proportion?

Suppose it is known that the income distribution in a particular region is right-skewed and bimodal. If bank economists are interested in estimating the mean income, which of the following is true?

What are the two assumptions and three conditions for the distribution of sample proportions? Explain each of them.

A major textbook publisher has a contract with a printing company. Part of the contract stipulates that no more than 5 percent of the pages should have any type of printing error. Suppose that the company selects a random sample of 400 pages and finds 33 that have an error. If the printer is meeting the standard, what is the probability that a sample of this size would have 33 or more errors?

Consider the following to answer the question(s) below: The owner of a small convenience store is trying to decide whether to discontinue selling magazines. He suspects that only 5% of the customers buy magazines and thinks that he might be able to sell something more profitable. Before making a final decision, he keeps track of the number of customers who buy magazines each day. On a typical day he has 280 customers in his store. -On a typical day, what would be the mean number of customers who buy magazines?

Which of the following statements is consistent with the Central Limit Theorem?