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NARA [144]
3 years ago
6

Delta Airlines quotes a flight time of 2 hours for its flights from Cincinnati to Tampa, meaning that an on-time flight would ar

rive in 2 hours. Suppose we believe that actual flight times are uniformly distributed between 1 hour 50min minutes and 135 minutes.a. Show the graph of the probability density function for flight time.b. What is the probability that the flight will be no more than 5 minutes late?c. What is the probability that the flight will be more than 10 minutes late?d. What is the expected flight time?

Mathematics
1 answer:
ddd [48]3 years ago
6 0

Answer:

a) Attached

b) P=0.60

c) P=0.80

d) The expected flight time is E(t)=122.5

Step-by-step explanation:

The distribution is uniform between 1 hour and 50 minutes (110 min) and 135 min.

The height of the probability function will be:

h=\frac{1}{Max-Min}=\frac{1}{135-110} =\frac{1}{25}

Then the probability distribution can be defined as:

f(t)=\frac{1}{25}=0.04 \,\,\,\,\\\\t\in[110,135]

b) No more than 5 minutes late means the flight time is 125 or less.

The probability of having a flight time of 125 or less is P=0.60:

F(T

c) More than 10 minutes late means 130 minutes or more

The probability of having a flight time of 130 or more is P=0.80:

F(T>t)=1-0.04(t-110)\\\\F(T>130)=1-0.04*(130-110)=1-0.04*20=1-0.8=0.2

d) The expected flight time is E(t)=122.5

E(t)=\frac{1}{2}(max+min)= \frac{1}{2}(135+110)=\frac{1}{2}*245=122.5

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