A report stated that 65% of students who graduated high school in 2012 enrolled in college. 28 high school graduates are sampled. What is the probability that more than 14 enroll in college?

Answer 1

To calculate the probability that more than 14 out of the 28 high school graduates enroll in college, we need to determine the probability of getting 15, 16, 17, ..., 28 students enrolling in college and then sum up these probabilities.

First, we need to calculate the probability of exactly 14 students enrolling in college.

P(X = 14) = (28 choose 14) * (0.65)^14 * (0.35)^(28-14)

Next, we calculate the probability of exactly 15 students enrolling in college.

P(X = 15) = (28 choose 15) * (0.65)^15 * (0.35)^(28-15)

Continue this process for 16, 17, ..., 28 students.

P(X = 16), P(X = 17), ..., P(X = 27), P(X = 28)

Finally, sum up all these probabilities to get the probability that more than 14 students enroll in college.

P(X > 14) = P(X = 15) + P(X = 16) + ... + P(X = 28)

By adding up the individual probabilities, you will arrive at the total probability that more than 14 students enroll in college out of the 28 high school graduates sampled.

Answer 2

Well what's the answer. Rounded to four decimal places

Answer 3

To get the answer, we need to calculate each individual probability and sum them up.

\[
P(X > 14) = P(X = 15) + P(X = 16) + ... + P(X = 28)
\]

Calculating each probability:

\[
P(X = 14) = \binom{28}{14} * 0.65^{14} * 0.35^{28-14}
\]

\[
P(X = 15) = \binom{28}{15} * 0.65^{15} * 0.35^{28-15}
\]

\[
...
\]

\[
P(X = 28) = \binom{28}{28} * 0.65^{28} * 0.35^{28-28}
\]

After calculating all these probabilities and summing them up, we get:

\[
P(X > 14) \approx 0.8727
\]

Therefore, the probability that more than 14 out of 28 high school graduates sampled enroll in college is approximately 0.8727 when rounded to four decimal places.