A study of college students stated that 25% of all college students have at least one tattoo. In a random sample of 80 college students, let x be the number of the students that have at least one tattoo. Find the mean and standard deviation for this binomial distribution.
A) Mean = 20, Standard Deviation = 3.87
B) Mean = 80, Standard Deviation = 15
C) Mean = 20, Standard Deviation = 15
D) Mean = 80, Standard Deviation = 3.87

Question

Quizplus · Accepted Answer

The mean of a binomial distribution is calculated as n * p, and the standard deviation is sqrt(n * p * (1-p)). Here, n = 80 and p = 0.25, so the mean is 80 * 0.25 = 20, and the standard deviation is sqrt(80 * 0.25 * 0.75) ≈ 3.87.

A Study of College Students Stated That 25% of All