91Ó°ÊÓ

Student scores on exams given by a certain instructor have mean 74 and standard deviation \(14 .\) This instructor is about to give two exams, one to a class of size 25 and the other to a class of size \(64 .\) (a) Approximate the probability that the average test scorc in the class of sizc 25 cxcceds \(80 .\) (b) Repeat part (a) for the class of size 64 (c) Approximate the probability that the average test score in the larger class exceeds that of the other class by over 2.2 points. (d) Approximate the probability that the average test score in the smaller class exceeds that of the other class by over 2.2 points.

An insurance company has 10,000 automobile policyholders. The expected yearly claim per policyholder is \(\$ 240,\) with a standard deviation of \(\$ 800\) Approximate the probability that the total yearly claim cxcccds \(\$ 2.7\) million.