36 percent of all customers who enter a store will make a...

36 percent 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. (1) Use the binomial formula to calculate the probability that exactly five customers make a purchase. (Round your answer to 4 decimal places.) Probability (2) Use the binomial formula to calculate the probability that at least three customers make a purchase. (Round your answer to 4 decimal places.) Probability (3) Use the binomial formula to calculate the probability that two or fewer customers make a purchase. (Round your answer to 4 decimal places.) Probability (4) Use the binomial formula to calculate the probability that at least one customer makes a purchase. (Round your answer to 4 decimal places.) Probability

Transcript

00:01 In this question we are looking at a binomial distribution, and we want to use the binomial formula.

00:07 So we need two parameters, n the number of independent trials, which here is 6, p the probability of success, which here is 36%, 0 .36.

00:20 So we're going to use the binomial formula, which is the probability of exactly x purchases out of 6 is equal to n to 2.

00:30 Choose x, p to the x, 1 minus p to the n minus x.

00:36 And for part one, we want the probability that exactly five of them make a purchase.

00:43 So probability of the x is exactly five.

00:47 So we have five of them make a purchase, which we call successes, and one of them does not.

00:54 This term is for the five that do make purchases.

00:57 Each one has a probability of 0 .36, and because these are in independent, we can combine them by just multiplying the probabilities.

01:06 So we take 0 .36.

01:08 For each of these, multiply it by itself five times.

01:12 This term is for the one that does not make a purchase, a probability of 0 .64.

01:19 If they're not in the 36 % that make a purchase, they're in the 64 % that did not.

01:24 Okay, so this is now the probability that the first five people make a purchase and the last one does not.

01:31 That's five out of six, but it's not the only way that might happen.

01:36 Perhaps the first three make a purchase, the fourth does not, the last two do.

01:41 This also has the same probability here, but it's a different simple outcome.

01:47 We need to account for all possible orders here.

01:50 This term tells you how many orders there are.

01:53 It comes from combinations.

01:55 So it's a number of unique ways to put these in orders.

01:58 It's called six choose five, which is just six.

02:00 Now we multiply these three terms together, and we will get our solution, which is 0 .2, 2, 2, 2 to 4 decimal places.

02:22 Okay, next part 2, at least 3.

02:26 So our formula will tell us the probability of an exact number, and now we want at least 3.

02:33 So we're going to have to find, so x is at least 3, we're going to find the probability of 3, probability of 4, probability of 5, which we already have, with a probability of 6, making purchases, and we'll add all of these together to get the total probability of at least 3.

02:53 Okay, so we need to just fill out the information here...

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