Question

Suppose 38% of recent college graduates plan on pursuing a graduate degree. Twenty recent college graduates are randomly selected.

a. What is the probability that no more than four of the college graduates plan to pursue a graduate degree? (Do not round intermediate calculations. Round your final answers to 4 decimal places.)

b. What is the probability that exactly five of the college graduates plan to pursue a graduate degree? (Do not round intermediate calculations. Round your final answers to 4 decimal places.)

c. What is the probability that at least eight but no more than thirteen of the college graduates plan to pursue a graduate degree? (Do not round intermediate calculations. Round your final answers to 4 decimal places.)

Answer 1

This is a binomial distribution

p = 0.38

n = 20

P(X = x) = 20Cx * 0.38^x * (1 - 0.38)^20-x

a) P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

                  = 20C0 * 0.38⁰ * 0.62²⁰ + 20C1 * 0.38¹ * 0.62¹⁹ + 20C2 * 0.38² * 0.62¹⁸ + 20C3 * 0.38³ * 0.62¹⁷ + 20C4 * 0.38⁴ * 0.62¹⁶

                  = 0.0726

b) P(X = 5) = 20C5 * 0.38⁵ * 0.62¹⁵ = 0.0945

c) P(8 < X < 13) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13)

                          = 20C8 * 0.38⁸ * 0.62¹² + 20C9 * 0.38⁹ * 0.62¹¹ + 20C10 * 0.38¹⁰ * 0.62¹⁰ + 20C11 * 0.38¹¹ * 0.62⁹ + 20C12 * 0.38¹² * 0.62⁸ + 20C13 * 0.38¹³ * 0.62⁷

                         = 0.5070