Question

Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes. What is the probability that the flight will be no more than 5 minutes late?

Answer 1

0.5

Explanation:

Answer 2

Answer: 0.5

Explanation:

Given : Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa.

i.e. Flight time = 2(60) +5= 125 minutes [∵ 1 hour = 60 minutes]

Actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes.

i.e. In minutes the flight times are between 120 minutes and 140 minutes.

Let x be a uniformly distributed variable in [120 minutes, 140 minutes] that represents the flight time.

Since the probability density function for x uniformly distributed in [a,b] is
`f(x)=(1)/(b-a)`

⇒ Probability density function for flight time :
`(1)/(140-120)=(1)/(20)`

5 minutes late than usual time = Flight time+ 5 = 125+5 = 130 minutes

Now , the probability that the flight will be no more than 5 minutes late will be :-

`\int^(130)_(120) (1)/(20)\ dx\\\\=(1)/(20)[x]^(130)_(120)\\\\= (130-120)/(20)\\\\=(1)/(2)=0.5`

Hence, the probability that the flight will be no more than 5 minutes late is 0.5.