Question

Q41 Johnny X owns a gift shop in New York. Last year she evaluated that the probability of a customer who says they are just browsing, buys something, is 30%. Suppose that on a particular day this year 15 customers browse in the store each hour. [8 Marks]

Assuming a binomial distribution, respond to the following questions:

(a) Develop the individual probability distribution histogram for all the possible outcomes.

(b) What is the probability that at least one customer, who says they are browsing, will buy something during a specified hour?

(c) What is the probability that at least four customers, who say they are browsing, will buy something during a specified hour?

(d) What is the probability that no customers, who say they are browsing, will buy something during a specified hour?

e) What is the probability that no more than four customers, who say they are browsing, will buy something during a specified hour?

DO NOT WRITE THE ANSWERS - USE WORD FORMAT.

NO PLAGIARISM PLEASE

Answer 1

n = 15, p = 0.3, q = 1 - p = 0.7 P(x) = C(n, x) p^x q^(n - x) P(x) = C(15, x) 0.3^x 0.7^(15 - x) (a) (b) P(x ≥ 1) = 1 - P(0) = 1 - 0.0047 = 0.9953 (c) P(x ≥ 4) = 1 - [P(0) + P(1) + P(2) + P(3)] = 1 - [0.0047 + 0.0305 + 0.0916 + 0.1700] = 0.7031 (d) P(0) = 0.0047 (e) P(x ≤ 4) = P(0) + P(1) + P(2) + P(3) + P(4) = 0.0047 + 0.0305 + 0.0916 + 0.1700 + 0.2186 = 0.5155.