The random variable Y is the number of major hurricanes for a randomly selected year between 1851 and 2012. 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.

0 0.185 5 0.056 10.296 6 0.037 2 0.266 7 0.012 3 0.093 8 0.006 4 0.049