Question

Score data from a statewide exam for 10th-graders follows a normal distribution, has a mean of 90 , and has a standard deviation of 7.8. According to the Empirical Rule, 34% of test scores fall into what range? select all that apply

Below 82.2


below 82.2 and above 97.8


between 82.2 and 90


below 90


between 90 and 97.8


above 90


above 97.8

Answer 1

Between 82.2 and 90

Between 90 and 97.8

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 = 90

Standard deviation = 7.8.

According to the Empirical Rule, 34% of test scores fall into what range?

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

The normal distribution is symmetric, which means that 68/2 = 34% fall between one standard deviation of the mean and the mean and 34% fall within the mean and one standard deviation above the mean.

90 - 7.8 = 82.2

90 + 7.8 = 97.8

34% between 82.2 and 90

34% between 90 and 97.8

So the correct options are:

Between 82.2 and 90

Between 90 and 97.8