Simulated observations. Most statistical software packages have routines for simulating values of variables having specified distributions. Use your statistical software to generate 25 observations from the N(30, 5) distribution.

Compute the mean and standard deviation x and s of the 25 values you obtain. How close are x and s to the μ

and σ of the distribution from which the observations were drawn?

Repeat 19 more times the process of generating 25 observations from the N(30, 5) distribution and recording x and s. Make a stemplot of the 20 values of x and another stemplot of the 20 values of s. Make Normal quantile plots of both sets of data.

Briefly describe each of these distributions. Are they symmetric or skewed? Are they roughly Normal? Where are their centers?

(The distributions of measures like x and s when repeated sets of observations are made from the same theoretical distribution will be very important in later chapters.)