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 $3.5 million.
A) Approximately 0
B) 0.0228
C) 0.9772
D) Approximately 1

Question

Quizplus · Accepted Answer

We need to use the central limit theorem since we have a sample size larger than 30. The mean and standard deviation of the distribution of sample means can be calculated as follows:

mean = $3.26 million
standard deviation = $1.2 million / sqrt(100) = $0.12 million

To find the probability that the mean salary of the 100 players exceeded $3.5 million, we can standardize the sample mean:

z = ($3.5 million - $3.26 million) / $0.12 million = 2

Using a standard normal distribution table or calculator, we find the probability that z is greater than 2 to be approximately 0.0228. Therefore, the approximate probability that the mean salary of the 100 players exceeded $3.5 million is 0.0228.

Major League Baseball Salaries Averaged $3