Question

n a recent poll of female college students, 70% stated that they plan to graduate with a STEM degree. A math teacher at ODU decides to randomly sample 15 female college students. Find the probability that exactly 6 out of the 15 plan to graduate with a STEM degree. Round your answer to 4 decimal places.

Answer 1

Answer:

0.0116

Step-by-step explanation:

This problem can be treated as a binomial probability model with probability of success (graduating with a STEM degree) p = 0.70.

The probability of exactly 6 successes in n = 15 trials is given by:

$P(X=6) = \frac{n!}{(n-6)!6!}*p^x*(1-p)^{n-x}\\P(X=6) = \frac{15!}{(15-6)!6!}*0.7^6*(1-0.7)^{15-6}\\P(X=6) = 0.0116$

The probability that exactly 6 out of the 15 plan to graduate with a STEM degree is 0.0116.