Question

Suppose that past history shows that 60% of college students prefer brand c cola. a sample of 5 students is to be selected. based on the binomial probability distribution, the probability that more than 3 prefer brand c is ________.

Answer 1

The probability is 0.337.

The probability that more than 3 prefer brand c is the same as finding the probability that 4 or 5 prefer brand c.  Using a binomial distribution,

$_5C_4(0.6)^4(0.4)^{5-4}+_5C_5(0.6)^5(0.4)^{5-5} \\ \\=\frac{5!}{4!1!}(0.6)^4(0.4)^1+\frac{5!}{5!0!}(0.6)^5(0.4)^0 \\ \\=5(0.6)^4(0.4)+1(0.6)^5(1)=0.33696\approx0.337$