The random variable Y is the sum of the dice when two balanced dice are rolled. Its probability distribution is as follows.

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 5.10 on page 219.
c. Draw a probability histogram for the random variable; locate the mean; and show one-, two-, and three-standard-deviation intervals.

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y 2 3 4 5 67 8 9 10 11 12 36 18 12 9 36 6 36 9 12 18 36