Question

According to a survey by the AdministrativeManagement Society, one-half of U.S. companies giveemployees 4 weeks of vacation after they have beenwith the company for 15 years. Find the probability that among 7companies surveyed at random, thenumber that give employees 4 weeks of vacation after15 years of employment is(a)anywhere from 4 to 6(b) Fewerthan 3

Answer 1

p = 0.5

n = 7

This is a binomial distribution.

P(X = x) = 7Cx * 0.5^x * (1 - 0.5)^7-x

a) P(4 < X < 6) = P(X = 4) + P(X = 5) + P(X = 6)

                        = 7C4 * 0.5⁴ * 0.5³ + 7C5 * 0.5⁵ * 0.5² + 7C6 * 0.5⁶ * 0.5¹

                        = 0.4922

b) P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

                  = 7C0 * 0.5⁰ * 0.5⁷ + 7C1 * 0.5¹ * 0.5⁶ + 7C2 * 0.5² * 0.5⁵

                  = 0.2266