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 was no more than $3.0 million.

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 $3.0 million is ($3.0 million - $3.26 million) / $0.12 million = -2.17. Using the standard normal distribution table, the probability of a z-score less than -2.17 is approximately 0.0151.

Major League Baseball Salaries Averaged $3