Question

# Thirty percent (30%) of all customers who enter a store will make a purchase. Suppose that...

Thirty percent (30%) of all customers who enter a store will make a purchase. Suppose that 6 customers enter the store and that these customers make independent purchase decisions. Let x be the number of the 6 customers who will make a purchase.

Use the binomial formula to calculate

1. The probability that exactly 2 customers make a purchase.
2. The probability that 2 or fewer customers make a purchase.
3. The probability that at least 1 customer makes a purchase

Answer: Thirty percent (30%) of all customers who enter a store will make a purchase. Suppose that 6 customers enter the store and that these customers make independent purchase decisions. Let x be the number of the 6 customers who will make a purchase.

Solution:

X ~ Bin(6, 0.30)

Using the binomial distribution,

P(X = x) = nCx * p^x * (1-p)^n-x

Therefore,

The probability that exactly 2 customers make a purchase = 0.3241

The probability that 2 or fewer customers make a purchase = 0.7743

The probability that at least 1 customer makes a purchase = 0.8823