Question 8.110

79. Use the information in Exercise 77 and your result from Exercise 78 to answer these questions.

  1. What is the standard deviation of the number of days in the past four that a randomly chosen 19- to 25-year-old has worked out?
  2. You interview 100 randomly chosen 19- to 25-year olds. You ask each how many days in the past four he or she has worked out, and you calculate the average number of days. According to the central limit theorem, there is a probability of 0.95 that your average will fall between what two values?

79.

(a) The variance is calculated as follows:

Thus, the standard deviation is days.

(b) The sampling distribution of is approximately normal with and standard deviation . Applying the 68−95−99.7 rule: with probability 0.95, values of x lie in the interval (0.54, 1.00).