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

Answer:

0.5

Step-by-step explanation:

Answer 2

Answer:  0.5

Step-by-step 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 $f(x)=\dfrac{1}{b-a}$

⇒ Probability density function for flight time  : $\dfrac{1}{140-120}=\dfrac{1}{20}$

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 :-

$\int^{130}_{120} \dfrac{1}{20}\ dx\\\\=\dfrac{1}{20}[x]^{130}_{120}\\\\= \dfrac{130-120}{20}\\\\=\dfrac{1}{2}=0.5$

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