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. 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 $4.0 million is ($4.0 million - $3.26 million) / $0.12 million = 6.17. A z-score of 6.17 is extremely high, making the probability of the sample mean exceeding $4.0 million approximately 0.

Major League Baseball Salaries Averaged $3