Question

1)A real estate agent has 20 properties that she shows. She feels that there is a 440% chance of selling any one property during a week. The chance of selling any one property is independent of selling another property. Compute the probability of selling less than 5 properties in one week. Round your answer to four decimal places.

2)Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.

P(X=14) , n=19 , p=0.6

Answer 1

1) p = 0.4

n = 20

This is a binomial distribution

P(X = x) = 20Cx * 0.4^x * (1 - 0.4)^20-x

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

              = 20C0 * 0.4⁰ * 0.6²⁰ + 20C1 * 0.4¹ * 0.6¹⁹ + 20C2 * 0.4² * 0.6¹⁸ + 20C2 * 0.4³ * 0.6¹⁷ + 20C4 * 0.4⁴ * 0.6¹⁶

              = 0.051

2) p = 0.6

n = 19

P(X = 14) = 19C14 * 0.6¹⁴ * 0.4⁵ = 0.0933