module 5 and exam
Problem Set 5.1
Problem Set 5.1
1. Describe, in your own words the sampling distribution of x̄.
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2. For the sampling distribution of x̄, is it necessary that the samples used in the distribution be all of the same size?
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3. What is E(x̄)? What is E(x̄) equal to?
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4. Suppose you take a random sample and find the sample mean, x̄. Based on the previous problem, can you say that x̄ is equal to the mean of the entire population µ?
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Problem Set 5.2
Problem Set 5.2
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?
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2. A nursing home has 2000 patients. You sample 170 patients. Can you use the infinite standard deviation formula?
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3. 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?
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4. 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?
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5. Suppose that you take a sample of size 40 from a population that is normally distributed. Can the sampling distribution of x̄ be approximated by a normal probability distribution? What if the population was not normally distributed, can the sampling distribution of x̄ be approximated by a normal probability distribution?
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Problem Set 5.3
Problem Set 5.3
1. 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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2. Suppose that in a certain large city, the mean 100 meter dash time for male high school seniors was reported to be 13.3 seconds with a standard deviation of 1.9 seconds. We may assume that the population is normally distributed.
a) What is the probability that 20 male high school seniors selected at random will have a mean 100 meter dash time of 12.5 seconds or less?
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b) What is the probability that 40 male high school seniors selected at random will have a mean 100 meter dash time of 12.5 seconds or less?
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c) What is the probability that 35 male high school seniors selected at random will have a mean 100 meter dash time between 13 seconds and 14 seconds?
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3. 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?
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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?
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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?
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Problem Set 5.4
Problem Set 5.4
1. 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?
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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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