Question

Suppose that 70% of the customers of a fast food chain order french fries how many of the next twenty customers who place an order expected to order french fries?

Answer 1

Answer:

14 of the next twenty customers who place an order expected to order french fries

Step-by-step explanation:

For each customers, there are only two possible outcomes. Either they order french fries, or they do not order french fries. The probability of a customer ordering french fries is independent from other customers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[\tex]In which [tex]C_{n,x}[\tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[\tex]And p is the probability of X happening.The expected value is given by:[tex]E(X) = np$

70% of the customers of a fast food chain order french fries

This means that $p = 0.7$

How many of the next twenty customers who place an order expected to order french fries?

This is E(X) when n = 20. So

$E(X) = np = 20*0.7 = 14$

14 of the next twenty customers who place an order expected to order french fries