Question

As a special promotion for its 20-ouce bottles of soda, a soft drink company printed a message on the inside of each bottle 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." Grayson's statistics class wonders if the comparty's claim holds true at a nearby convenience store.
To find out, all 30 students in the class go to the store and each buys one 20-ounce bottle of the soda.
Two of the students in Grayson's class got caps that say, "You're a winner!" Does this result give convincing evidence that the company's 1-in-6 claim is false?

A) Yes. If the "1 in 6 wins" claim is true, there is a 10.28% probability that two or fewer students would win a prize.
Because this outcome is not very unlikely, we have convincing evidence that the company's claim is false.

B) Yes. If the "1 in 6 wins" claim is true, there is a 89.72% probability that two or fewer students would win a prize.
Because this outcome is not very unlikely, we do not have convincing evidence that the company's claim is false.

C) No. If the "1 in 6 wins" claim is true, there is a 10.28% probability that two or fewer students would win a prize.
Because this outcome is not very unlikely, we do not have convincing evidence that the company's claim is false.

D) Yes. Only 6.67% of the students won a prize and 16.67% were supposed to win a prize.

E) No. If the "1 in 6 wins" claim is true, there is a 89.72% probability that two or fewer students would win a prize.
Because this outcome is not very unlikely, we have convincing evidence that the company's claim is false.

Answer 1

According to the probability calculations, there is not enough evidence to support or reject the company's claim that 1 in 6 wins a prize.

Step-by-step explanation:

According to the information given, the company claims that 1 in 6 wins a prize. In Grayson's class, 30 students bought one 20-ounce bottle each, and 2 of them got caps that say, 'You're a winner!'. To determine if the company's claim is false, we need to calculate the probability of getting two or fewer winners if the claim is true.

To calculate this probability, we can use the binomial probability formula, which is P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2), where X is the number of winners. Assuming the claim is true, the probability of winning is 1/6. Plugging these values into the formula, we get P(X ≤ 2) = (1/6)^0 * (5/6)^(30-0) + (1/6)^1 * (5/6)^(30-1) + (1/6)^2 * (5/6)^(30-2).

Using a calculator to evaluate this expression, we find that P(X ≤ 2) ≈ 0.893 or 89.3%. Because this outcome (2 or fewer winners) is not very unlikely, we do not have convincing evidence to conclude that the company's claim is false. Therefore, the correct answer is B) No. If the '1 in 6 wins' claim is true, there is a 89.3% probability that two or fewer students would win a prize. Because this outcome is not very unlikely, we do not have convincing evidence that the company's claim is false.