Question

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?
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?

Answer 1

Explanation:

Let X be the no of customers who purchase atleast one item.

X is binomial since there are two outcomes and each customer is independent of the other.

a) Here n =10

Out of 10 customers we expect np = 3 customers to buy at least one item.

b) exactly 3 of the customers would purchase at least one item

=
`P(X=3)=10C3(0.3)^3(0,7)^7\\=0.2668`

c) the probability that no more than 3 customers would purchase at least one item

=
`P(X\leq 3)\\= 0.6496`