Question

Binomial problems: Basic
Anita's, a fast-food chain specializing in hot dogs and garlic fries, keeps track of the
proportion of its customers who decide to eat in the restaurant (as opposed to ordering the
food "to go"), so it can make decisions regarding the possible construction of in-store play
areas, the attendance of its mascot Sammy at the franchise locations, and so on. Anita's
reports that 48% of its customers order their food to go. If this proportion is correct, what
is the probability that, in a random sample of 4 customers at Anita's, exactly 3 order their
food to go?

Answer 1

This problem is dealing with the binomial distribution. The binomial distribution has a fixed number of trials (n) and has a probability of success (p). In this case a success is a customer ordering their food to go since that is what is being asked in part a.

First off, p needs to be in decimal form not a percent. To change it to a decimal you just take the number and divide by 100.

Now that you have done that you can solve part a. by taking the sample size (n) multiplied by the probability of a success (p)

Mean = n*p

To solve for part b. you need to use the formula for the standard deviation of a binomial distribution. This can be found by taking the square root of n*p*(1-p)

Standard Deviation = sqrt[n*p*(1-p)]