Question

PHSTAT ONLY!!!!

Instructions: Show your complete solution. Simply giving the final answer without showing your calculations will NOT merit any points. If you’re using PhStat or Excel calculations, upload the excel file. You can also cut and paste the Excel work output on a word file, and upload it here.

Major league baseball salaries averaged $3.41 million with a standard deviation of $1.25 million in a certain year in the past. Suppose a sample of 100 major league players was taken.

1. Calculate the standard error for the sample mean summary.
2. What is the probability that the mean salary of the players exceeded $3.5 million?
3. What is the probability that the mean salary of the players was less than $2.7 million.
4. What is the probability that the mean salary of the players was less than $2.5 million OR greater than $3.6 million?

Answer 1

Let , , n=100

We have , the sampling distribution of the sample mean is ,

1. The statnadard error for the sample mean is ,

2. Now ,

; The Excel function is , =1-NORM.DIST(0.72,0,1,TRUE)

OR

;

The Excel function is , =1-NORM.DIST(0.72,3.41,0.125,TRUE)

Therefore , the probability that the mean salary of the players exceeded $3.5 million is 0.2358

2.

; The Excel function is , =NORM.DIST(2.7,3.41,0.125,TRUE)

Therefore , the probability that the mean salary of the players was less than $2.7 million is 0.0000

3.

The Excel function is , =NORM.DIST(2.5,3.41,0.125,TRUE)+1-NORM.DIST(3.6,3.41,0.125,TRUE)

Therefore , the probability that the mean salary of the players was less than $2.5 million OR greater than $3.6 million is 0.0643