1) Salaries for major league baseball players averaged $1.5 million with a standard deviation of $.8 million in 1994. Suppose a sample of 100 major league players was taken. Find the approximate probability that the average salary of the 100 players exceeded $1.2 million
2) The tread of life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 8,300 miles. If the manufacturer warrants the tire for the first 45,000 miles, what proportion of the tires will need to be replaced under warranty? What if the warranty is for the first 40,000 miles?
3) A manufacturer considers a production lot unacceptable if 11% or more of the units in the lot are defective. In such cases the company wants to scrap the entire lot. A company quality control inspector has proposed the following criterion for determining whether to reject a lot: In a sample of 10 units from a lot, if two or more are defective, reject the entire lot. If the lot currently under examination is 11% defective, what is the probability that this decision rule will lead the quality control inspector to the correct decision?