Question

The points obtained by students of a class in a test are normally distributed with a mean of 60 points and a standard deviation of 5 points.
About what percent of students have scored between 60 and 65 points?

Answer 1

Answer:

Step-by-step explanation:

This fraction represents the area under the standard normal curve between 60 and 65 points.  This represents the area from the mean (60) to one standard deviation above the mean (65).  The applicable z-score is

       65 - 60

z = --------------- = 1.

             5

The problem then involves finding the area under the curve from z = 0 (that is, the mean) to z = 1 (one standard deviation above the mean).

Refer to the "empirical rule."  This rule states that 68% of data lies within one standard deviation of the mean, that is, within z = -1 and z = 1.  We are interested only in the area that is within z = 0 and z = 1, which is half of 68%, and thus is 34%.

In summary, approx. 34% of students have scored between 60 and 65 points.