Question

1. A recent Survey showed that residents of City A have the longest travel times to get to work compared to residents of other cities in North Carolina. According to the latest statistics available, the average travel time to work for residents of City A is 22.5 minutes. a. Assume the exponential probability distribution is applicable and show the probability density function for the travel time to work for a resident of this city. b. What is the probability it will take a resident of this city between 20 and 40 minutes to travel to work? c. What is the probability it will take a resident of this city more than 45 minutes to travel to work?

Answer 1

Solution or > . > Mean== - 1 22:5 o- I 22;5. a). The probability density function of exparential distribution f(x,0) - oë ox. p.d.f of his > f(x) = 1 e 275 :x30 22.5 b). Here we have to find the porobability that will Etake a resident of this city between 20 and 40 P (20 x 540) = P(X4 40) - PCX220) = (1-e 40|22:5). Cl-e-20/22:5).

= 0.8309 - 0.5888 - 10.2421) 2 P ( x >45) = |- P ( x 245). - 1-C1-e45/22-5) = é 45/22.5 -10.1357