Question

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

Answer 1

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:

$F(T<t)=0.04(t-min)\\\\F(T<125)=0.04*(125-110)=0.04*15=0.60$

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

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