SOLUTION: A population has a mean of 300 and a standard deviation of 18. A sample of 144 observations will be taken. The probability that the sample mean will be between 297 to 303 is: Su

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Question 623216: A population has a mean of 300 and a standard deviation of 18. A sample of 144 observations will be taken. The probability that the sample mean will be between 297 to 303 is:
Supposely the result is 0.8664 but i cant get the result for nothing... i get always 0.9545. How i get the other result?
I'd be greatful for some answer... normally i dont get any on this site :(
Thanks in advance
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

A population has a mean of 300 and a standard deviation of 18. A sample of 144 observations will be taken. 

The probability that the sample mean will be between 297 to 303 is:

Note: graph of Standard Normal Curve showing z = 0 and z = ±1, ±2, ±3 



In your Ex: P(297 < X < 303)

   P ( -3/18/12) < z < 3 /18/12)) = P ( 2 < z < 2) = .9545  

Agree with You.  

to get .8864, that would be P( -1.5 < z < 1.5) 

Using z = ± 1.5 would be incorrect thing to do in this case.

For the normal distribution: 

one  standard deviation from the mean accounts for about 68.2% of the set 

two standard deviations from the mean account for about 95.5%

and three standard deviations from the mean account for about 99.7%.