In an accounting class of 200 students, the mean and standard deviation of scores was 70 and 5, respectively. Use the empirical rule to determine the number of students who scored less than 65 or more than 75?

a. About 64
b. About 136
c. About 32
d. About 68

a. About 64

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 70

Standard deviation = 5

Use the empirical rule to determine the number of students who scored less than 65 or more than 75?

65 = 70 - 5

So 65 is one standard deviation below the mean

75 = 70 + 5

So 75 is one standard deviation above the mean.

By the Empirical Rule, 68% of the students scored between 65 and 75. The other 100-68 = 32% scored less than 65 or more than 75.

Out of 200, that is

0.32*200 = 64

So the correct answer is:

a. About 64