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.
1. Explain why X is a binomial random variable.
2. Find the mean of X. Interpret this value is context.
3. Find the standard deviation of X. Interpret this value is context.
4. 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 by chance alone and
use this result to support your answer.