Question

An airline estimates that 94% of people booked on their flights actually show up. If the airline books 68 people on a flight for which the maximum number is 66, what is the probability that the number of people who show up will exceed the capacity of the plane

Answer 1

0.0788

Explanation:

In this case the final probability will be the sum of the probability of when there are 67 more reserves when there are 68.

That is to say:

P (f) = P (x = 67) + P (x = 68)

n = 68; p = 0.94

Now we calculate each one:

P (x) = nCx * (p ^ x) * [(1 - p) ^ (n-x)]

nCx = n! / (x! * (n - x)!)

Knowing the formula, we replace:

P (67) = 68C67 * (0.94 ^ 67) * [(1 - 0.94) ^ (68-67)]

nCx = 68! / (67! * (68 - 67)!) = 68! / 67! = 68

P (67) = 68 * (0.0158) * (0.06) = 0.064

Now for x = 68

P (68) = 68C68 * (0.94 ^ 68) * [(0.0641 - 0.94) ^ (68-68)]

nCx = 68! / (68! * (68 - 68)!) = 1

P (68) = 1 * (0.0148) * (1) = 0.0148

Then replacing in the main formula:

P (f) = P (x = 67) + P (x = 68)

P (f) = 0.064 + 0.0148

P (f) = 0.0788