Question

The probability that a person who booked a flight will actually show up is 0.95. If the airline books 104 people on a flight for which the maximum capacity is 100, what is the probability that there will be enough seats for everyone who shows up? Round your answer to 3 decimal places.

Answer 1

X ~ Bin ( n , p)

Where n = 104 , p = 0.95

Mean= np = 104 * 0.95 = 98.8

SD = sqrt ( n p( 1 - p) ) = sqrt ( 104 * 0.95 ( 1 - 0.95 )) = 2.2226

Using normal approximation

P(X < x) = P(Z < ( x - mean) / SD )

With continuity correction

P(X <= 100 ) = P(Z < (100.5 - 98.8) / 2.2226)

= P(Z < 0.76)

= 0.776