Use a computer to generate a random sample of 500 values of a normally distributed variable x with a mean of 100 and a standard deviation of 20. Construct a histogram of the 500 values.

a. Use the computer commands on page 101 to randomly generate a sample of 500 data from a normal distribution with mean 100 and standard deviation 20. Construct a histogram using class boundaries that are multiples of the standard deviation 20; that is, use boundaries from 20 to 180 in intervals of 20 (see commands on pp. 61–62).

Let’s consider the 500 x values found in part a as a population.

b. Use the computer commands on pages 101–102 to randomly select a sample of 30 values from the population found in part a.

Construct a histogram of the sample with the same class intervals used in part a.

c. Repeat part b three times.

d. Calculate several values (mean, median, maximum, minimum, standard deviation, etc.) that describe the population and each of the four samples. (See p. 89 for commands.)

e. Do you think a sample of 30 data adequately represents a population? (Compare each of the four samples found in parts b and c to the population.)