Question

The mean points obtained in an aptitude examination is 159 points with a standard deviation of 13 points.

What is the probability that the mean of the sample would differ from the population mean by more than 1 point if 60 exams are sampled? Round your answer to four decimal places.
don't for get to round

Answer 1

`0.4514 = 45.14%`

Explanation:

Use the equation:

`Z=(X-u)/(a)`

Given:

`u=159, o=13,n=60,s=1.68`

This is the pvalue of Z when
`X = 159+1 = 160` subtracted by the pvalue of Z when
`X = 159-1 = 158`

`x = 160`

`Z=(X-u)/(o)`

Central Limit Theorem applied:

`Z=(X-u)/(o)`

`Z=(160-159)/(1.68)`

`Z=0.6`

`Z=0.6(\text{P-value}:0.7257)`

`X=150`

`Z=(X-u)/(o)`

`Z=(158-159)/(1.68)`

`Z=-0.6`

`Z=-6(\text{P-value}:0.2743`

`0.7257-0.2743=0.4514`

This means that there is a 45.14% probability.