In her MAT135 class, professor Alayeb found that the mean score of the first exam was 96. Suppose that the scores are normally distributed with a standard deviation of 19 points.

Question

What is the probability that a randomly selected score is less than 71? P(x < 71)=

Answer 1

Hi Xavier,

This problem involves the classic equation in introductory statistics:

z = (x - mu) / sigma

x= desired score

mu= mean

sigma= standard deviation

So:

x= 71

mu= 96

sigma= 19

z = (71 - 96) / 19

z = -1.32

From z-table:

P(Z< -1.32) = 0.0934

This is quite low, and it would make sense given how well students performed on that test on average. I hope this helps.