One year, the distribution of salaries for professional sports players had mean $1.6 million and standard deviation $0.7 million. Suppose a sample of 100 major league players was taken. Find the approximate probability that the average salary of the 100 players that year exceeded $1.1 million.
A) approximately 1
B) .2357
C) .7357
D) approximately 0

Question

Quizplus · Accepted Answer

The sample mean's distribution is normal with mean $1.6 million and standard deviation $0.07 million (0.7/√100). The z-score for $1.1 million is (1.1-1.6)/0.07 = -7.14, which is far in the left tail, making the probability of exceeding $1.1 million approximately 1.

One Year, the Distribution of Salaries for Professional Sports Players