Question

Delta Airlines quotes a flight time of 3 hours, 6 minutes for a particular flight. Suppose we believe that actual flight times are uniformly distributed between 3 hours and 3 hours, 48 minutes.

What is the probability that the flight will be no more than 6 minutes late?

Answer 1

Answer :

Given

1 hour = 60 mintues

then,

a = 3 hours = 3 * 60 = 180

b = 3hours 48 mintues

= (3 * 60 )+ 48

= 180 + 48

= 228 min

flight time = 3 hours 6 mintues.

= (3 * 60) + 6

= 180 + 6

= 186 min

Here the flight will be no more than 6 minutes late,

i.e X = 186 + 6 = 192 min

therefore,

Probability that the flight will be no more than 6 minutes late = P(X <= x)

So, P(X <= 192) = (x-a) / (b-a)

Where X = 192 , a = 180 , b = 228

P(X <= 192) = (192 - 180) / (228 - 180)

= 12 / 48

= 0.25

Probability that the flight will be no more than 6 minutes late = 0.25