Question

Trevor is interested in purchasing the local hardware/sporting goods store in the small town of Dove Creek, Montana. After examining accounting records for the past several years, he found that the store has been grossing over $850 per day about 60% of the business days it is open. Estimate the probability that the store will gross over $850 for the following. (Round your answers to three decimal places.)

(c) fewer than 5 out of 10 business days

(e) more than 17 out of the next 20 business days

Answer 1

p = 0.6

P(X = x) = nCx * 0.6^x * (1 - 0.6)^n-x

a) n = 10

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

              = 10C0 * 0.6⁰ * 0.4¹⁰ + 10C1 * 0.6¹ * 0.4⁹ + 10C2 * 0.6² * 0.4⁸ + 10C3 * 0.6³ * 0.4⁷ + 10C4 * 0.6⁴ * 0.4⁶

              = 0.1662

b) n = 20

P(X > 17) = P(X = 18) + P(X = 19) + P(X = 20)

                = 20C18 * 0.6¹⁸ * 0.4² + 20C19 * 0.6¹⁹ * 0.4¹ + 20C20 * 0.6²⁰ * 0.4⁰

                = 0.0036