Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year. Suppose a sample of 100 major league players was taken. Find the approximate probability that the mean salary of the 100 players exceeded $4.0 million.
A) Approximately 0
B) 0.0228
C) 0.9772
D) Approximately 1

Question

Quizplus · Accepted Answer

The standard error of the mean is $1.2 million / sqrt(100) = $0.12 million. The z-score for a mean salary of $4.0 million is (4.0 - 3.26) / 0.12 = 6.17. A z-score of 6.17 is extremely high, making the probability of the mean salary exceeding $4.0 million approximately 0.

Major League Baseball Salaries Averaged $3