Question

2. Binomial

Suppose according to past data for a small boutique, about 30% of the customers who walk into the store purchase at least one item.

a. Today 10 individual customers walked into the store while you are there. How many of these 10 customers do you expect would by at least one item? (hint: expected value formula)

b. What is the chance that exactly 3 of the customers would purchase at least one item?

 

c. What is the probability that no more than 3 customers would purchase at least one item? (Hint: sketch a table for the number of people who would purchase at least one item out of the 10. You do not need to put in all the probabilities, just all the values of X. For which values of X would you have to add the probabilities? Student who were in my BUS 90 class are familiar with this problem. Feel free to help your fellows on Canvas discussion this weekend.)

Answer 1

2) p = 0.3

n = 10

P(X = x) = 10Cx * 0.3^x * (1 - 0.3)^10-x

a) Expected value = n * p = 10 * 0.3 = 3

b) P(X = 3) = 10C3 * 0.3³ * 0.7⁷ = 0.2668

c) P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

                  = 10C0 * 0.3⁰ * 0.7¹⁰ + 10C1 * 0.3¹ * 0.7⁹ + 10C2 * 0.3² * 0.7⁸ + 10C3 * 0.3³ * 0.7⁷

                  = 0.6496