Thirty percent of all customers who enter a department store...

Thirty percent of all customers who enter a department store will make a purchase. Suppose that 6 customers enter the store and that these customers make independent purchase decisions. a. Find the probability that exactly 5 customers make a purchase. b. Find the probability that at least 3 customers make a purchase. c. Find the probability that two or fewer customers make a purchase. d. Find the probability that at least one customer makes a purchase. e. As the manager of the department store, how should store associates persuade customers who enter the store to make a purchase?

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00:02 All right.

00:03 So here we are given a binomial probability where there is a 30 % chance.

00:07 They make a purchase and we have a sample of six and they're independent.

00:11 So that tells us that it's binomial.

00:13 So the first one we're looking for, what is the probability that exactly five people make a purchase? so there are actually six ways of doing that.

00:21 So six choose five where we have 0 .3 to the fifth power and 0 .7 to the first power.

00:30 Also, i'm going to use my calculator function binomial pdf with an n of 6, a p of 0 .3, and an x of 5.

00:42 And that will do that formula for me.

00:45 So probability distributions, scroll down to binomial pdf, 6, 0 .3, and 5, and i get the probability 0 .02.

01:04 Part b, find the probability that at least three customers make a purchase.

01:11 And with a lot of calculators, it pays to do this one as one minus the probability it is less than or equal to two.

01:21 All right.

01:22 So, yeah, so another way of doing that is to tell one minus the probability of x greater than or equal to two, because most calculators will do that.

01:34 So i'm going to do one minus binomial cdf, n of 6, p of 0 .3, and x of 2.

01:44 It's because the binomial cdf takes away everything, every option that you put in and less than that...

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