Question

A social scientist claims that only 70% of all high school seniors capable of doing college work actually go to college. If a sample of 15 people are chosen, find probability that more than 13 people actually go to college.

Answer 1

The probability that a senior actually goes to college is 0.7. We use a binomial distribution and receive: $p=C_{15}^{13}(0.7)^{13}(0.3)^2+C_{15}^{14}(0.7)^{14}(0.3)+C_{15}^{15}(0.7)^{15}\approx0.11157$

The latter is rounded to 5 decimal places.

Answer: 0.11157