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.


  1. Explain why X is a binomial random variable.

  1. Find the mean of X. Interpret this value in context.

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

  1. 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.


Public Answer

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