Question

Suppose American Airlines quotes a flight time of 137 minutes for its flights from Irvine, CA to DFW.

Suppose we believe that actual flight times are uniformly distributed between 110 minutes and 160 minutes. Answer the following questions.

a. The probability density function between the range is defined as f(x)=  .

b. Compute the probability that a flight from Irvine, CA to DFW will be more than 10 minutes late from its quoted time. P=(X>147)=  

c. Compute the probability that its actual flight time will be the exactly same as its quoted time, 137 minutes. P=(X=137)=  

d. Compute the mean flight time.

Answer 1

X = A flight time of 137 minutes for its flight from Irvine, CA to DFW

PDF:

f(x) = 1/160 -110 , 110 < x < 160

= 0 , otherwise

f(x) = 1/50 ,110< x < 160

= 0 , otherwise

f(x) = 0.02 , 110< x < 160

= 0 , otherwise

ii)  

P(X > 147) =

= 0.02x

= 0.02(160 - 147)  

= 0.02(13)

= 0.26

iii)

P(X = 137) = 0.02 since X is uniformly distributed between 110 and 160

iv)  

Mean of uniform distribution is given by

E(X) = (b + a)/2

E(X) = (160 + 110)/2

= 270/2

= 135

or

E(X) =  

=   

= 0.02x²/2

= 0.01x²

= 0.01(160² - 110²)

= 0.01(25600 - 12100)

= 0.01(13500)

= 135

Note

if X is uniformly distributed between a and b then

f(x) = 1/(b -a) , a< x< b

= 0 , otherwise

Mean of X or E(X) = (b +a)/2