Question

The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For this question, DO NOT apply the standard deviation rule.

(a) What proportion of the students scored at least 25 points on this test, rounded to five decimal places?

(b) What is the 29 percentile of the distribution of test scores, rounded to three decimal places?

Answer 1

Solution

The given information as follow

Mean = = 22

SD = = 2

a)

proportion of the students scored at least 25 points =

Z score :

= 1 - value of z to the left of 1.5

= 1 - 0.93319 = 0.06681

b)

We have to find 29 percentile of the distribution.

So value of z with 0.29 area to the left from z table = - 0.553