Thirty percent of all customers who enter a store will make

Thirty percent of all customers who enter a store will make a purchase. Suppose six customers enter the store and that these customers make independent purchase decisions, Let x = the number of the six customers who will make a purchase. Write the binomial formula for this situation. Use the binomial formula to calculate The probability that exactly five customers make a purchase.

Solution

.3 of all customers make a purchase
.7 of all customers don\'t make a purchase

P(x = 5) = 6C5 * .3^5 * .7
P(x = 5) = 0.010206
P(x = 5) = 1.02%

P(x = 3 or 4 or 5)
P(3) = 6C3 * .3^3 * .7^3
P(4) = 6C4 * .3^4 * .7^2
P(5) = 6C5 * .3^5 * .7

P(x >= 3) = 0.18522 + 0.059535 + 0.010206
P(x >= 3) = 0.254961
P(x >= 3) = 25.5%

P(x <= 2)
P(0) = .7^6
P(1) = 6C1 * .3 * .7^5
P(2) = 6C2 * .3^2 * .7^4
P(x <= 2) = P(0 + 1 + 2)

P(x >= 1) = 1 - .7^6

.3 came from the first sentence in your quesiton. Thirty percent of all customers make a purchase
30% = .3 make a purchase
.7 don\'t