# the normal distribution question help

• Apr 25th 2012, 01:54 PM
dkrstic79
the normal distribution question help
Hi,

I am new here, and I hope you can help.

Here is the question:

One year, the distribution of salaries for professional sports players had mean \$1.5 million and standard deviation \$0.9 million. Suppose a sample of 400 major leagu0e players was taken. Find the approximate probability that the average salary of the 400 players that year exceeded \$1.1 million.

The correct answer is approximately 1, but I can't figure out how to work it out.

So far I have tried resolving it by following
z= 1,100,000-1,500,000/900,000 = 0.4 which according to the z table translates to .1554

Then I subtracted this number from .5 which resulted in .3446 which I take it to mean that approximately 34% of players earn more than 1.1million.

How do I use the 400 baseball players in this equation?

Thanks
• Apr 25th 2012, 09:35 PM
biffboy
Re: the normal distribution question help
The standard deviation of sample means = 0.9/sqrt400
• Apr 26th 2012, 06:12 AM
dkrstic79
Re: the normal distribution question help
0.9 / sqrt(400) = 0.045

but...I still don't know how to solve the original question. How do I get to the answer that approximately 1 player's salary exceeds 1.1 million? Please be as explicit as possible.

thanks.
• Apr 26th 2012, 06:29 AM
biffboy
Re: the normal distribution question help
The question asks for the P that the average salary of 400 players exceeds 1.1

So we want P(Z> (1.1-1.5)/0.045) That is P(Z>-8.89) which from tables is approx. 1
• Apr 26th 2012, 06:47 AM
dkrstic79
Re: the normal distribution question help
thank you so much