One year, the distribution of salaries for professional sports players had mean $1.8 million and standard deviation $0.6 million. Suppose a sample of 400 major league players was taken. Find the approximate probability that the average salary of the 400 players that year exceeded $1.1 million.
A) approximately 1
B) approximately 0
C) .2357
D) .7357

Question

Quizplus · Accepted Answer

The sample mean's distribution will be approximately normal due to the Central Limit Theorem. The standard error is 0.6 million / sqrt(400) = 0.03 million. The z-score for 1.1 million is (1.1 - 1.8) / 0.03 = -23.33, which is extremely low, indicating a probability close to 1 that the sample mean exceeds 1.1 million.

One Year, the Distribution of Salaries for Professional Sports Players