Question

As a special promotion for its 16-ounce bottles of fruit juice, a juice drink 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 seven wins a prize!" Suppose the company is telling the truth and that every 16-ounce bottle of juice has a one-in-seven chance of being a winner. Eight friends each buy one 16-ounce bottle of juice 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 two of the friends win a prize. Is this group of friends just lucky? Or is the company's one-in-seven claim inaccurate? Compute P(X ≥ 2) and use the result to justify your answer. (3 points) (10 points)

Answer 1

Part A: As we are given here that every one in seven wins a prize, therefore each of the event here is independent and identically distribution and therefore this is a case of a binomial distribution given as:

Part B: The mean and standard deviation of X here is computed as:

Part C: The required probability here is computed as:

As the probability here is greater than 0.05, therefore the event is not that rare and therefore it is not like the friends are lucky or the company's claim one in seven is inaccurate. The event is very likely.