Question 5. Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in 2009. Suppose a sample of 100 major league players was taken.

a) What was the standard error for the sample mean salary? (Explain/show how you obtain your answer.) (4 pts.)

b) Find the approximate probability that the mean salary of the 100 players exceeded $3.5 million. (Explain/show how you obtain your answer.) (4 pts.)

c) Find the approximate probability that the mean salary of the 100 players exceeded $4.0 million. (Explain/show how you obtain your answer.) (4 pts.)

d) Find the approximate probability that the mean salary of the 100 players was no more than $3.0 million. (Explain/show how you obtain your answer.) (4 pts.)

e) Find the approximate probability that the mean salary of the 100 players was less than $2.5 million. (Explain/show how you obtain your answer.) (4 pts.)

Question 6. At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken.

a) What is the standard error for the sample mean? (Explain/show how you obtain your answer.) (5 pts.)

b) What is the probability that the sample mean will be between 0.99 and 1.01 centimeters? (Explain/show how you obtain your answer.) (5 pts.)

c) What is the probability that the sample mean will be below 0.95 centimeters? (Explain/show how you obtain your answer.) (5 pts.)

d) Above what value do 2.5% of the sample means fall? (Explain/show how you obtain your answer.) (5 pts.)