Name : Hour :. Date : Analyzing Binomial Random Variables Important ideas from the text :" Free lunch ? 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 . 2 . Find the mean of X . Interpret this value in context . 3 . Find the standard deviation of X . Interpret this value in 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 just by chance and use this result to support your