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 was no more than $3.0 million.
A)approximately 0
B)0.0151
C)0.9849
D)approximately 1

Question

Quizplus · Accepted Answer

We need to use the central limit theorem since the sample size is large enough (n=100) and we do not know the population standard deviation.

z = (x̄ - μ) / (σ / √n)
z = (3.0 - 3.26) / (1.2 / √100)
z = -2.1667

Using a standard normal distribution table or calculator, we find that the probability of obtaining a z-score of -2.1667 or less is approximately 0.0151, which corresponds to answer choice B.

Major League Baseball Salaries Averaged $3