Question

He cafeteria at Midtown Middle School surveyed 575 students about their favorite food. If 8% of the students surveyed liked chicken, how many students said that chicken is their favorite food?

Answer 1

46.08 students said that chicken is their favorite food.

Explanation:

Let X denote the number of students who liked chicken.

The proportion of students who liked chicken is, p = 0.08.

About n = 576 students were surveyed about their favorite food.

Every student's answer was independent of the others.

Thus, the random variable X follows a binomial distribution with parameters n = 576 and p = 0.08.

The probability mass function of X is:

`P(X=x)={576\choose x}(0.08)^(x)(1-0.08)^(576-x);\ x=0,1,2,3...576`

Then expected number of students who said that chicken is their favorite food is:

`E(X)=np\\\\=576*0.08\\\\=46.08`

Thus, 46.08 students said that chicken is their favorite food.