Question

Twenty five individuals are randomly selected out of 100 shoppers leaving a local bedding store. Each shopper was asked if they made a purchase during their visit. Each of the shoppers has the same probability of answering ‘yes’ to having made a purchase. The probability that exactly four of the twenty-five shoppers made a purchase could best be found by

Answer 1

we have 25 individuals that are randomly selected out of 100 shoppers leaving a local bedding store, and we know that each of the shoppers has the SAME probability of answering yes to having made a purchase, so we can assume that the probability that a person or a shopper made a purchase is 1 / 12.

Also we know that we selected 25 individuals, so there are 25 shoppers that can say yes, that means our sample size N is 25.

and you want to know the probability that exactly 4 of the 25 shoppers made a purchase

this is a binomial distribution because we can see that we have a sample size n = 25, we have a proportion of success, 1/2to say yes to having made a purchase and we can say that each shopper is independently from the other shoppers.

So the binomial equation is given by:  (check the attached image)

so we know that we want P(X=4) because we want to know exactly 4 out of 25.

so n is 25, p is 1/2 and x is 4 so substituting the values into the equation we will get:

P(X=4) = 25C4 * (1/2)^4 * (1 - 1/2)^(25-4)

P(X=4) = 12650 * 0.0625 * 0.000000476

P(X=4) = 0.000377

the probability that exactly 4 of the 25 shoppers made a purchase is....0.00010243