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

Question

Quizplus · Accepted Answer

We are given the population mean, standard deviation, and sample size. Since the sample size is large enough (n=100), we can use the Central Limit Theorem to approximate the distribution of the sample mean as normal with mean = population mean and standard deviation = population standard deviation / sqrt(n).

Thus, the z-score corresponding to a sample mean of $3.0 million is:

z = (3.0 - 3.26) / (1.2 / sqrt(100)) = -2.833

Using a standard normal table or calculator, we can find that the probability of getting a sample mean no more than $3.0 million is approximately 0.0151.

Therefore, the correct answer is B.

Major League Baseball Salaries Averaged $3