I have these problems due tomorrow - any help is greatly appreciated
1. Suppose that a brewery has a filling machine that fills 12 oz bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean 12.32 oz and a standard deviation of 0.04 oz. Find the probability that a bottle contains between 12.22 and 12.28 oz.
2. One year, pro sports players salaries averaged $1.5 million with a standard deviation of $0.6 million. Suppose a sample of 400 major league players was taken. Find the approximate probability that the average salary of the 400 players exceeded $1.1 million.
3. Assume that the salaries of elementary school teachers in the US are normally distributed with a mean of $32,000 and a standard deviation of $6,000. What is the cutoff salary for teachers in the bottom 10%?
4. The tread life of a particular brand of tire is a random variable best described by a normal distribution with mean of 60,000 miles and a standard deviation of 1,400 miles. What warranty should the company use if they want 96% of the tires to outlast the warranty?