Find the indicated probability. Round to three decimal places.
-An airline estimates that 91% of people booked on their flights actually show up. If the airline books 76 people on a flight for which the maximum number is 74, what is the probability that the Number of people who show up will exceed the capacity of the plane?
A) 0.028
B) 0.006
C) 0.007
D) 0.001

Question

Quizplus · Accepted Answer

The problem can be modeled using a binomial distribution with n = 76 and p = 0.91. We need to find the probability that more than 74 people show up, i.e., P(X > 74). This can be calculated using the complement rule: P(X > 74) = 1 - P(X ≤ 74). Using a binomial calculator or statistical software, P(X ≤ 74) is approximately 0.993, so P(X > 74) is approximately 0.007.

Find the Indicated Probability