Question

Forty percent of all undergraduates at a university are chemistry majors. In a random sample of six students, find the probability that exactly two are chemistry majors. 12. The probability that exactly two are chemistry majors is Type an integer or a decimal. Round to four decimal places as needed.)

Answer 1

0.3110

Explanation:

This is a binomial distribution with probability of success (being a chemistry major) p = 0.40.

The general formula for a binomial distribution is:

`P(x=k)=(n!)/((n-k)!k!)*p^k*(1-p)^(n-k)`

Where n is the sample size and k is the desired number of successes.

The probability of k=2 in a sample of n =6 is:

`P(x=2)=(6!)/((6-2)!2!)*0.4^2*(1-0.4)^(6-2) \\P(x=2)=(6!)/((6-2)!2!)*0.4^2*(1-0.4)^(6-2)\\P(x=2)=3*5*0.4^2*0.6^4\\P(x=2)=0.3110`

The probability is 0.3110