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

Answer:

46.08 students said that chicken is their favorite food.

Step-by-step 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:

$E(X)=np\\\\=576\times0.08\\\\=46.08$

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