Answer to Question #335945 in Statistics and Probability for Sami

Question

A recent study by the American Accounting Association revealed among 30 graduates in accounting 20 students graduating with a major in accounting select public accounting. Suppose we select a sample of 15 recent graduates.

What is the probability that exactly two select public accounting?

What is the probability that exactly five select public accounting?

Answer 1

$X\sim Bin(n, p)$

Given $n=15, p=0.23, q=1-p=0.77$

a.

$$P(X=2)=\dbinom{15}{2}(0.23)^2(0.77)^{15-2}$$

$$\approx0.18579088281$$

b.

$$P(X=5)=\dbinom{15}{5}(0.23)^5(0.77)^{15-5}$$

$$\approx0.1416125568$$