Answer to Question #297381 in Statistics and Probability for Leyman

Question

A mean of 3 out of 5 students request for tomato sauce with their meal in a canteen. A random sample of 8 students is selected, what is the probability that less than 4 students request for tomato sauce with their meal?

Answer 1

Let $X=$ the number of students request for tomato sauce with their meal in a cantee: $X\sim Bin(n, p).$

Given $n=8, p=3/5=0.6, q=1-p=1-0.6=0.4.$

i)

$$P(X<4)=P(X=0)+P(X=1)$$

$$+P(X=2)+P(X=3)$$

$$=\dbinom{8}{0}(0.6)^0(0.4)^{8-0}+\dbinom{8}{1}(0.6)^1(0.4)^{8-1}$$

$$+\dbinom{8}{2}(0.6)^2(0.4)^{8-2}+\dbinom{8}{3}(0.6)^3(0.4)^{8-3}$$

$$=0.00065536+0.00786432$$

$$+0.04128768+0.12386304$$

$$=0.1736704$$