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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

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MrRoyal

Answer:

[tex]Mean = 2392.5[/tex]

[tex]SD = 44.70[/tex]

Step-by-step explanation:

Given

[tex]Students = 14500[/tex]

[tex]p = 16.5\%[/tex]

Solving (a): The mean

Mean is calculated as thus:

[tex]Mean = np[/tex]

[tex]Mean = 16.5\% * 14500[/tex]

Convert % to decimal

[tex]Mean = 0.165 * 14500[/tex]

[tex]Mean = 2392.5[/tex]

Solving (b): The Standard Deviation

Standard deviation (SD) is calculated as thus:

[tex]SD = \sqrt{np(1-p)}[/tex]

[tex]SD = \sqrt{14500 * 16.5\%(1-16.5\%)}[/tex]

Convert % to decimal

[tex]SD = \sqrt{14500 * 0.165 * (1-0.165)}[/tex]

[tex]SD = \sqrt{14500 * 0.165 * 0.835}[/tex]

[tex]SD = \sqrt{1997.7375}[/tex]

[tex]SD = 44.6960568731[/tex]

[tex]SD = 44.70[/tex]

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