Question

The assistant manager of a surf shop estimates that 65% of customers will make a purchase. Part A: How many customers should a salesperson expect until he finds a customer that makes a purchase? Part B: What is the probability that a salesperson helps 3 customers until he finds the first person to make a purchase?

Answer 1

Answer:

A) 2

B) 0.239

Step-by-step explanation:

Part A) Expected value of a binomial distribution is the number of trials times the probability of success.

X = np

Given X = 1 and p = 0.65:

1 = 0.65n

n = 1.54

Rounding up, a salesperson should expect 2 customers until he finds a customer that makes a purchase.

Part B) Use binomial probability.

P = nCr pʳ qⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1−p).

Given n = 3, r = 1, p = 0.65, q = 0.35.

P = ₃C₁ 0.65¹ 0.35³⁻¹

P ≈ 0.239

Or, using binompdf function in a calculator:

binompdf(n, p, r)

= binompdf(3, 0.65, 1)

≈ 0.239