Question

The mean age of the students in this class is 15.75. The standard deviation is 1.55. Determine the number of standard deviations from the mean required to include

of the ages listed.
13, 17, 18, 15, 16, 14, 15, 18, 17, 16, 15, 16, 13, 15, 17, 17

Answer 1

To determine the number of standard deviations from the mean required to include x% of the ages, we can use the empirical rule (also known as the 68-95-99.7 rule).

Step-by-step explanation:

To determine the number of standard deviations from the mean required to include x% of the ages, we can use the empirical rule (also known as the 68-95-99.7 rule).

For example, to find the number of standard deviations required to include 95% of the ages, we look at the empirical rule. Between 34% and 13.5% of the ages will be more than one standard deviation below the mean, and between 34% and 13.5% of the ages will be more than one standard deviation above the mean. Therefore, to include 95% of the ages, we need to go approximately two standard deviations below and above the mean.

In this particular case, we can find the number of standard deviations from the mean required to include x% of the ages by multiplying the standard deviation by the appropriate number of standard deviations (e.g., for 95% confidence level, multiply by 2).