Question: 1 in 6 wins As a special promotion for its 20-ounce bottles of soda, a soft drink company printed a message on the inside of each cap. Some of the caps said, "Please try again," while others said, "You're a winner!" The company advertised the promotion with the slogan "1 in 6 wins a prize." Suppose the company is telling the truth and that every 20-ounce bottle of soda it fills has a 1-in-6 chance of being a winner. Seven friends each buy one 20-ounce bottle of the soda at a local convenience store. Let X = the number who win a prize.
(a) Explain why X is a binomial random variable.
(b) Find the mean and standard deviation of X. Interpret each value in context.
(c) The store clerk is surprised when three of the friends win a prize. Is this group of friends just lucky, or is the company's 1-in-6 claim inaccurate? Compute P(X ≥ 3) and use the result to justify your answer.