Elly's hot dog emporium is famous for its chilidogs. Some customers order the hot dogs with hot peppers, while many do not care for that added bit of zest. Elly's latest sales indicate that 30% of the customers ordering her chili dogs order it with hot peppers. Suppose 18 customers are selected at random. What is the probability that between two and six people inclusive want hot peppers?

Question

Quizplus · Accepted Answer

This problem can be solved using the binomial distribution with n=18 and p=0.3. We want to find the probability that between two and six people inclusive want hot peppers, which can be expressed as P(2 <= x <= 6). We can use the binomial probability formula or a binomial probability table to find the individual probabilities of each value of x, and then add them together. Using a calculator or software, we get:

P(2 <= x <= 6) = P(x=2) + P(x=3) + P(x=4) + P(x=5) + P(x=6)
= 0.0416 + 0.1211 + 0.1856 + 0.2001 + 0.1609
= 0.7093

Therefore, the probability is 0.708, which is closest to choice C.

Elly's Hot Dog Emporium Is Famous for Its Chilidogs