Question 6.21

6.21 Increasing sample size.

Heights of adults are well approximated by the Normal distribution. Suppose that the population of adult U.S. males has mean of 69 inches and standard deviation of 2.8 inches.

  1. What is the probability that a randomly chosen male adult is taller than 6 feet?
  2. What is the probability that the sample mean of two randomly chosen male adults is greater than 6 feet?

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  3. What is the probability that the sample mean of five randomly chosen make adults is greater than 6 feet?
  4. Provide an intuitive argument as to why the probability of the sample mean being greater than 6 feet decreases as gets larger.

6.21

(a) 0.1423. (b) 0.0643. (c) 0.0082. (d) It becomes less likely to have a sample mean greater than 6 ft. because as the sample size increases we are more likely to get a few short males in our sample, which will pull the mean closer to the population mean, which is 69 in.