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# Exercise 6.2

1.
The scores on a general test have mean 450 and standard deviation 50. It is highly desirable to score over 480 on this exam. A person can get into Smith's College prestigious MBA program if he/she scores over 480. In one location 25 people sign up to take the exam. The average score of these 25 people exceeds 490. Is this odd? Should the test center investigate? Answer on the basis of the CLT.
2.
A machine fills cereal boxes at a factory. Due to an accumulation of small errors (different flakes sizes, etc.) it is thought that the amount of cereal in a box is normally distributed with mean 22 oz. for a supposedly 20 oz. box. Suppose the standard deviation of the amount filled is 1.3 oz. A federal regulatory selects four of these boxes at random and finds that the average content of these boxes is less than 18 oz. This official knows that the company claims the mean content to be 22 oz. He promptly fines the company. Who is right? Use the CLT in your answer.
3.
Sixteen adult males are in a pit which is 98 feet deep. They decide to stand on one another (feet to head), hoping that the person on top can grip the top of the pit and get out, and, hence go for help. What's the probability that their plan succeeds? (Ans: .0003).

Next: Exercise 7.1 Up: No Title Previous: Exercise 6.1

2000-08-26