The random variable X is the crew size of a randomly selected shuttle mission between April 12, 1981 and July 8, 2011. Its probability distribution is as follows.

We have provided the probability distributions of the random variables considered in Exercises 5.11-5.15 of Section 5.1. For each exercise, do the following tasks.
a. Find and interpret the mean of the random variable.
b. Obtain the standard deviation of the random variable by using one of the formulas given in Definition 5.5.
c. Construct a probability histogram for the random variable; locate the mean; and show one-, two-, and three-standard-deviation intervals.

4 P(X-x0.030 0.022 0.267 0.207 0.467 0.007