Question

Research has revealed that forty percent of Internet company employees have stock options in their companies. Consider a random sample of 12 employees from an Internet company, (a) What is the probability that at least 7 employees have stock options in the company? What is the mean number of Internet company employees who have stock options in their companies, in a sample of 12 employees? What is the probability that at most 7 employees will not have stock in the company? (Hint: Note that "success" here has changed in problem (c.)}

Answer 1

a) p = 0.4

n = 12

P(X > 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)

              = 12C7 * 0.4⁷ * 0.6⁵ + 12C8 * 0.4⁸ * 0.6⁴ + 12C9 * 0.4⁹ * 0.6³ + 12C10 * 0.4¹⁰ * 0.6² + 12C11 * 0.4¹¹ * 0.6¹ + 12C12 * 0.4¹² * 0.6⁰

              = 0.1582

b) Mean = n * p = 12 * 0.4 = 4.8

c) p = 1 - 0.4 = 0.6

P(X > 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)

              = 12C7 * 0.6⁷ * 0.4⁵ + 12C8 * 0.6⁸ * 0.4⁴ + 12C9 * 0.6⁹ * 0.4³ + 12C10 * 0.6¹⁰ * 0.4² + 12C11 * 0.6¹¹ * 0.4¹ + 12C12 * 0.6¹² * 0.4⁰

              = 0.6652