Use the following information to answer the question. Suppose that the probability that a person books a hotel using an online travel website is 0.68. For the questions that follow, consider a sample of fifteen randomly selected people who recently booked a hotel.
-What is the probability that at least fourteen out of fifteen people used an online travel website when they booked their hotel? Round to the nearest thousandth.
A)0.323
B)0.022
C)0.978
D)0.028

Question

Quizplus · Accepted Answer

The probability of at least 14 out of 15 people using an online travel website is the complement of the probability of 13 or fewer people using an online travel website. The probability of 13 or fewer people using an online travel website is the sum of the probabilities of 0, 1, 2, ..., 13 people using an online travel website. This can be calculated using the binomial distribution with n = 15 and p = 0.68. The probability of 13 or fewer people using an online travel website is 0.022. Therefore, the probability of at least 14 out of 15 people using an online travel website is 1 - 0.022 = 0.978.

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