Australian football salaries averaged $150,000 with a standard deviation of $80,000 in a recent year.Suppose a sample of 100 football players was taken.Find the approximate probability that the average salary of the 100 players exceeded $100,000.
A) Approximately 1
B) 0.2357
C) 0.7357
D) Approximately 0

Question

Quizplus · Accepted Answer

Given the large sample size (n=100), we can use the Central Limit Theorem to approximate the distribution of the sample mean. The mean salary is $150,000 with a standard deviation of $80,000. The standard error of the mean (SEM) is the standard deviation divided by the square root of the sample size, which is $80,000/√100 = $8,000. To find the probability that the average salary exceeds $100,000, we calculate the Z-score for $100,000, but since this value is significantly below the mean, the probability of the sample mean exceeding $100,000 is very high, approaching 1.

Australian Football Salaries Averaged $150,000 with a Standard Deviation of $80,000