Find the indicated probability. Round to four decimal places.
-An airline estimates that 93% of people booked on their flights actually show up. If the airline books 73 people on a flight for which the maximum number is 71, what is the probability that the
Number of people who show up will exceed the capacity of the plane?
A)0.0275
B)0.0325
C)0.1070
D)0.0050

Question

Find the indicated probability. Round to four decimal places.
-An airline estimates that 93% of people booked on their flights actually show up. If the airline books 73 people on a flight for which the maximum number is 71, what is the probability that the
Number of people who show up will exceed the capacity of the plane? 
A)0.0275
B)0.0325
C)0.1070
D)0.0050

Quizplus · Accepted Answer

The probability that more than 71 people show up can be calculated using the binomial distribution or a normal approximation to the binomial distribution. Given the high probability of showing up (93%) and the number of trials (73 bookings), the normal approximation is suitable. The mean number of people showing up is 73 * 0.93 = 67.89, and the standard deviation is sqrt(73 * 0.93 * 0.07) ≈ 2.4899. To find the probability of more than 71 people showing up, we calculate the z-score for 71.5 (for continuity correction) and use the standard normal distribution. The calculation yields a probability close to 0.0325, making option B the correct choice.

Find the Indicated Probability