Question

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.

Answer 1

Answer:

The mean for this binomial distribution is 20 students.

The standard deviation for this binomial distribution is 3.873 students.

Step-by-step explanation:

We can model this random variable with a binomial distribution with parameters n=80 (sample size) and p=0.25 (probability of having at least one tatoo).

Let x be the number of students that have at least one tatoo, the mean and standard deviation of x can be calculated as:

$\mu_x=n\cdot p=80\cdot 0.25=20\\\\\sigma_x=\sqrt{np(1-p)}=\sqrt{80\cdot0.25\cdot0.75}=\sqrt{15}=3.873$