Question

Scores on an exam are normally distributed with a mean of 76 and a standard deviation of 10. In a group of 230 tests, how many students score below 66?

Answer 1

37 students

Explanation:

Scores from an exam are normally distributed with a mean of 76 and a standard deviation of 10. Suppose 230 students take the exam. About how many would receive a score below 66?

First, determine the number of standard deviations that data score of 66 is from the mean.

To determine the x-axis values, subtract the standard deviation from the mean 76 repeatedly.

76 − 10 = 66

66 − 10 = 56

56 − 10 = 46

The scores that are below 66 are −2 and −3 standard deviations from the mean.

Add the percentages.

2.5% + 13.5% = 16%

About 16% of the scores are less than 66. Now find 16% of 230 students.

0.16(230) = 36.8

About 37 students would receive a score below 66.

Answer 2

z score = 66 - 76
---------- = - 1
10

from the tables of normal distribution this corresponds to 0.34-3 of the area under the normal curve
so reuired number od students = 0.3413 * 230 = 78