Question

The student body of a large university consists of 60% female students. A random sample of 8 students is selected. Refer to Exhibit 5-8. What is the probability that among the students in the sample at least 6 are male?

Answer 1

Answer:

0.0499

Step-by-step explanation:

This is a binomial probability  function expressed as:

$P(X=x)={n\choose x}p^x(1-p)^{n-x}$

Given that n =8, and p(male)=1-0.6=0.4, the probability of at least 6 being male is calculated as:

$P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X\geq 6)=P(X=6)+P(X=7)+P(X=8)\\\\={8\choose 6}0.4^6(0.6)^{2}+{8\choose 7}0.4^7(0.6)^{1}+{8\choose 8}0.4^8(0.6)^{0}\\\\=0.0413+0.0079+0.0007\\\\=0.0499$

Hence, the probability of at least 6 males is 0.0499