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.
7. Explain why X is a binomial random variable.
8. There are 10 winners on the first day of the promotion. What is the probability of this
occurring?
9. Find the mean of X. Interpret this value in context.
10. Find the standard deviation of X. Interpret this value in context.