Questions: What is the probability that more than 15 enroll in college?

Transcript text: College bound: A national college researcher reported that $66 \%$ of students who graduated from high school enrolled in college. Twenty nine high school graduates are sampled. Round the answers to four decimal places. Part 1 of 4 (a) What is the probability that exactly 17 of them enroll in college? The probability that exactly 17 of them enroll in college is 0.1060 . Part 2 of 4 (b) What is the probability that more than 15 enroll in college?

Solution

Solution Steps

Step 1: Probability of Exactly 17 Enrolling

To find the probability that exactly 17 out of 29 high school graduates enroll in college, we use the binomial probability mass function (PMF). Given that the probability of a student enrolling in college is $ p = 0.66 $, we calculate:

\[ P(X = 17) = 0.1060 \]

Step 2: Probability of More Than 15 Enrolling

Next, we calculate the probability that more than 15 students enroll in college. This is found by subtracting the cumulative probability of 15 or fewer students from 1:

\[ P(X > 15) = 1 - P(X \leq 15) = 0.9209 \]