As a special promotion for its 16-ounce bottles of water, a water company printed a message on the inside of each cap. Some of the caps read, "Better luck next time!" whereas others read, "You won!" The company advertised the promotion with the slogan "One in eight wins a prize!" Suppose the company is telling the truth and that every 16-ounce bottle of water has a one-in-eight chance of being a winner. Nine friends each buy one 16-ounce bottle of water at a local convenience store. Let X equal the number of friends who win a prize.

Part A: Explain why X is a binomial random variable. (3 points)

Part B: Find the mean and standard deviation of X. Interpret each value in context. (4 points)

Part 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 one-in-eight claim inaccurate? Compute P(X ≥ 3) and use the result to justify your answer.