Question

Assume all variables are binomial. (Note: If values are not found in Table B of Appendix C, use the binomial formula.)

High School Dropouts Approximately 10.3% of American high school students drop out of school before graduation. Choose 10 students entering high school at random. Find the probability that

a. No more than two drop out

b. At least 6 graduate

c. All 10 stay in school and graduate

Source: www.infoplease.com

Answer 1

From the given information, let X be the high school students drop out of school before graduation.

The probability that American high school students drop out of school before graduation be

Let the number of students chosen entering high school be

The probability mass function of a binomial distribution is,

(a)

Compute the probability that no more than 2 dropouts.

Therefore, the probability that no more than 2 dropouts is 0.9245.

(b)

Compute the probability that at least 6 high school students drop out of school.

Therefore, the probability that at least 6 high school students drop out of school is 0.0002.

(c)

Compute the probability that all 10 stay in school and graduate.

Therefore, the probability that all 10 stay in school and graduate is approximately 0.