Provide an appropriate response.
-One year, professional sports players salaries averaged $\$ 1.6$ million with a standard deviation of $\$ 0.7$ million. Suppose a sample of 100 major league players was taken. Find the approximate probability that the average salary of the 100 players exceeded $\$ 1.1$ million.
A) approximately 1
B) approximately 0
C) $0.2357$
D) $0.7357$

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 of the sample means is \$1.6 million, and the standard deviation of the sample means (standard error) is $\frac{\$0.7\ million}{\sqrt{100}} = \$0.07\ million$. To find the probability that the average salary exceeds \$1.1 million, we calculate the z-score for \$1.1 million and find the corresponding probability. However, since \$1.1 million is significantly below the mean (\$1.6 million), the probability that the sample mean exceeds \$1.1 million is very high, approaching 1.

Provide an Appropriate Response $1.6\$ 1.6$1.6 Million with a Standard Deviation Of

Provide an Appropriate Response $\$ 1.6$ Million with a Standard Deviation Of