a. Let X denote the age of a randomly selected undergraduate student at UWEC. Obtain the probability distribution of the random variable X. Display the probabilities to six decimal places.

b. Obtain a probability histogram or similar graphic for the random variable X.

c. Determine the mean and standard deviation of the random variable X.

d. Simulate 100 observations of the random variable X.

e. Roughly, what would you expect the average value of the 100 observations obtained in part (d) to be? Explain your reasoning.

f. In actuality, what is the average value of the 100 observations obtained in part (d)? Compare this value to the value you expected, as answered in part (e).

g. Consider the experiment of randomly selecting 10 UWEC undergraduates with replacement and observing the number of those selected who are 21 years old. Simulate that experiment 1000 times.

h. Referring to the simulation in part (g), in approximately what percentage of the 1000 experiments would you expect exactly 3 of the 10 students selected to be 21 years old? Compare that percentage to the actual percentage of the 1000 experiments in which exactly 3 of the 10 students selected are 21 years old.

Recall from Chapter 1 (see page 34) that the Focus database and Focus sample contain information on the undergraduate students at the University of Wisconsin - Eau Claire (UWEC). Now would be a good time for you to review the discussion about these data sets. The following problems are designed for use with the entire Focus database (Focus). If your statistical software package won't accommodate the entire Focus database, use the Focus sample (Focus Sample) instead. Of course, in that case, your results will apply to the 200 UWEC undergraduate students in the Focus sample rather than to all UWEC undergraduate students