M5 Problem Set

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Portage Learning *

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110

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Economics

Date

Jan 9, 2024

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6

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Uploaded by ProfessorPonyMaster1003

M5: Problem Set Question 1 Suppose that you are attempting to estimate the weight of 600 parts. In order to use the infinite standard deviation formula, what sample size, n, should you use? Question 2 Suppose that you take a sample of size 15 from a population that is known to be normally distributed. Can the sampling distribution of x̄ be approximated by a normal probability distribution?
Question 3 Suppose that you take a sample of size 20 from a population that is not normally distributed. Can the sampling distribution of x̄ be approximated by a normal probability distribution?
Question 4 Suppose a pharmaceutical company wants to do a study of the commissions of its sales force. Let's assume that there are 4,300 sales people and the population mean for the sales force is $52,400 in commissions and has a population standard deviation of $3,500. What is the probability that a simple random sample of 50 members of the sales force will have commissions within $400 of the population mean?
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Question 5 Suppose that you have a large number of potatoes. The mean weight of the potatoes is 7.4 ounces with a standard deviation of 2.2 ounces. We may assume a normal distribution. a) If you choose 25 potatoes at random, what is the probability that the mean of this sample of 25 potatoes is between 7 and 8 ounces? b) If you choose 45 potatoes at random, what is the probability that the mean of this sample of 45 potatoes is less than 7 ounces? c) If you choose 40 potatoes at random, what is the probability that the mean of this sample of 40 potatoes is more than 7.5 ounces?
Question 5 Answer
Question 6 According to the American Diabetes Association (2013), 8.3 % of the U.S. population have diabetes. a) Suppose that you take a random of 80 Americans, what is the probability that 7 % or less of these 80 people have diabetes? b) Suppose that you take a random of 120 Americans, what is the probability that 8 % or more of these 120 people have diabetes?
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