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 [tex]f(x)=\dfrac{1}{b-a}[/tex]
⇒ Probability density function for flight time : [tex]\dfrac{1}{140-120}=\dfrac{1}{20}[/tex]
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 :-
[tex]\int^{130}_{120} \dfrac{1}{20}\ dx\\\\=\dfrac{1}{20}[x]^{130}_{120}\\\\= \dfrac{130-120}{20}\\\\=\dfrac{1}{2}=0.5[/tex]
Hence, the probability that the flight will be no more than 5 minutes late is 0.5.
