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:
[tex]\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[/tex]
