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

It can be easily verified that m 4.66 and s 1.20.

a. Because m s 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?

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

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* x 1 2 3 4 5 6 7 p(x) .02 .03 .09 .25 .40 .16 .05