Question

A study of time spent traveling by car between Atlanta and Pembroke showed an approximately uniform distribution between 280 and 300 minutes. (a) What is the probability that the commuting time will be between 285 and 290 minutes? (Round answer to two decimal places.) (b) What is the probability that the commuting time will be less than 295 minutes? (Round answer to two decimal places.) (c) What are the mean and standard deviation of the travel time? (Round answers to four decimal places.) show your work.

Answer 1

a)

Here, the given values of lower limit, a = 280 and upper limit, b = 300

For Uniform Distribution,
P(x1 <= X <= x2) = (x2 - x1)/(b - a)
P(285 <= X <= 290) = (290 - 285)/(300 - 280)
P(285 <= X <= 290) = 0.25

b)

Here, the given values of lower limit, a = 280 and upper limit, b = 300

For Uniform Distribution,
P(X <= x) = (x - a)/(b - a)
P(X <= 295) = (295 - 280)/(300 - 280)
P(X <= 295) = 0.75

c)

Here, the given values of lower limit, a = 280 and upper limit, b = 300
For Uniform distribution,
Mean = (a + b)/2
Mean = (280 + 300)/2 = 290

Standard Deviation = sqrt((b - a)^2/12)
Standard Deviation = sqrt((300 - 280)^2/12 = 5.7735