Question

A national study found that 44% of college students engage in binge drinking. Using the 68-95-99.7 rule to describe the sampling distribution of a randomly selected group of 200 college students who engage in binge drinkning.

Answer 1

The sampling distribution of a randomly selected group of 200 college students who engage in binge drinking can be described using the 68-95-99.7 rule.

Step-by-step explanation:

The sampling distribution of a randomly selected group of 200 college students who engage in binge drinking can be described using the 68-95-99.7 rule, also known as the empirical rule.

This rule states that for a normally distributed variable, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

Since the national study found that 44% of college students engage in binge drinking, the sampling distribution of a randomly selected group of 200 college students who engage in binge drinking would have a mean of 44% and a standard deviation of:

Standard Deviation = (√(P(1-P))/n)

Substituting the values, we get:

Standard Deviation = (√(0.44(1-0.44))/200)

Standard Deviation ≈ 0.0356

Answer 2

`\bf \sigma = 0.0351`

Step-by-step explanation:

68–95–99.7 Rule : It also known as the empirical rule and it is a shorthand used to calculate the percentage of values that lie within a range around the mean in a normal distribution with the width of several standard deviation

μ = π = sample proportion

= 44 %

= 0.44

Population standard deviation proportion,

`\sigma = \sqrt{(\pi * (1 - \pi))/(n)}\\\\\implies \sigma= \sqrt{(0.44 * (1 - 0.44))/(200)}\\\\\implies\bf \sigma = 0.0351`