7.31 Exercise 7.8 gave the following probability distribution for x 5 the number of courses for which a randomly selected student at a certain university is registered:

x 1 2 3 4 5 6 7 p(x) .02 .03 .09 .25 .40 .16 .05 It can be easily verified that m 5 4.66 and s 5 1.20.

a. Because m 2 s 5 3.46, the x values 1, 2, and 3 are more than 1 standard deviation below the mean. What is the probability that x is more than 1 standard deviation below its mean? (Hint: See Example 7.13.)

b. What x values are more than 2 standard deviations away from the mean value (either less than m 2 2s or greater than m 1 2s)?

c. What is the probability that x is more than 2 standard deviations away from its mean value?