Question

In the 2017 national Youth Risk Behavior Survey, 16.5% of high school students had ridden with a driver who had been drinking alcohol within the previous month. This data came from an SRS of 14,500 students. what is the mean and standard deviation

Answer 1

`Mean = 2392.5`

`SD = 44.70`

Explanation:

Given

`Students = 14500`

`p = 16.5\%`

Solving (a): The mean

Mean is calculated as thus:

`Mean = np`

`Mean = 16.5\% * 14500`

Convert % to decimal

`Mean = 0.165 * 14500`

`Mean = 2392.5`

Solving (b): The Standard Deviation

Standard deviation (SD) is calculated as thus:

`SD = √(np(1-p))`

`SD = √(14500 * 16.5\%(1-16.5\%))`

Convert % to decimal

`SD = √(14500 * 0.165 * (1-0.165))`

`SD = √(14500 * 0.165 * 0.835)`

`SD = √(1997.7375)`

`SD = 44.6960568731`

`SD = 44.70`