**QUESTION**

A local fast-food restaurant is running a “Draw a three, get it free” lunch promotion. After each customer orders, a touch-screen display shows the message “Press here to win a free lunch.” A computer program then simulates one card being drawn at random from a standard deck of playing cards. If the chosen card is a 3, the customer’s order is free. (Note that the probability of drawing a 3 from a standard deck of playing cards is 4/52.) Otherwise, the customer must pay the bill. Suppose that 250 customers place lunch orders on the first day of the promotion. Let *X *= the number of people who win a free lunch.

- Explain why
*X*is a binomial random variable.

- Find the mean of
*X*. Interpret this value in context.

- Find the standard deviation of
*X*. Interpret this value in context.

- One of the customers is surprised when only 10 people win a free lunch. Should the customer be surprised? Find the probability that 10 or fewer people win a free lunch just by chance and use this result to support your answer.