Question

The amount of time it takes a FedEx semi-truck to travel from Austin, TX to Miami, FL is distributed as a uniform random variable between 2 hours, 45 minutes to 3 hours, 30 minutes.

a) The probability that that this semi-truck will take less than 3 hours, 15 minutes to travel from Austin, TX to Miami, FL today is ____ .

(Report your answer to 4 decimal places, using conventional rounding rules)

b) The probability that this semi-truck will take between 2 hours, 50 minutes and 3 hours, 8 minutes to travel from Austin, TX to Miami, FL today is ____ .

(Report your answer to 4 decimal places, using conventional rounding rules)

c) What is the standard deviation of this probability distribution?____ .

(Report your answer to 2 decimal places, using conventional rounding rules)

Answer 1

let x follow wiform diet as Xu ul 165, 210 minutes Pl X{195) f(x)= 165<x< 210 210 -165 45 fral- 165222210 45 ow 195 795 Pex< 195= [2] 45 45 165 165 0.6667 195- 165 30 45 45 PL 170 <x< 180)= 1188 La = 45 188 45 170 170 [188-1707 45 45 R Standard deviation & 161 = (210-165² 45. = 12.99 = 12.99