My teacher gave us the answers to questions. The answer to this question is 0.087 but I get .2970. Can you please tell me what I am doing wrong?
An airline estimates that 85% of people booked on their flights actually show up. If the airline books 16 people on a flight for which the maximum number is 14, what is the probability that the number of people who show up will exceed the capacity of the place? Is it unusual that 15 people will show up for the flight?
Probability of showing up: 85% = 0.85
Probability of not showing up: 1 - 0.85 = 0.15
P(exceeds the capacity)
= P(15 people show up) + P(16 people show up)
= (16C15)(0.85^15)(0.15^1) + (16C16)(0.85^16)(0.15^0)
= (16)(0.85^15)(0.15) + (1)(0.85^15)(1)
= .2970
An airline estimates that 85% of people booked on their flights actually show up. If the airline books 16 people on a flight for which the maximum number is 14, what is the probability that the number of people who show up will exceed the capacity of the place? Is it unusual that 15 people will show up for the flight?
Probability of showing up: 85% = 0.85
Probability of not showing up: 1 - 0.85 = 0.15
P(exceeds the capacity)
= P(15 people show up) + P(16 people show up)
= (16C15)(0.85^15)(0.15^1) + (16C16)(0.85^16)(0.15^0)
= (16)(0.85^15)(0.15) + (1)(0.85^15)(1)
= .2970