Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in
A certain year in the past.Suppose a sample of 100 major league players was taken.Find the
Approximate probability that the mean salary of the 100 players exceeded $3.5 million.

Question

Quizplus · Accepted Answer

The sampling distribution of the sample mean will be approximately normal with mean $3.26 million and standard deviation $1.2 million/sqrt(100) = $0.12 million. The z-score for $3.5 million is (3.5 - 3.26) / 0.12 = 2. The probability that the mean exceeds $3.5 million is the probability that a standard normal variable exceeds 2, which is approximately 0.0228.

Major League Baseball Salaries Averaged $3