Question

Suppose you are waiting at the bus stop in The Neighborhood, and the probability of the next bus towards Town Square arriving in the next x hours is uniformly distributed between 3 and 5 hours.

a. What are the mean and standard deviation of the distribution? (round to 4 decimal places when necessary)

b. What is the probability of the bus arriving between the next 3.75 to 4.5 hours? (don’t round)

Answer 1

SOLUTION:

Solution :

Given that,

a = 3

b =5

MEAN = a+b / 2=3+5/2=4

standard deviation =  (b - a)2 / 12 = (5 - 3)2 / 12 = 0.58

b.

P(c< x < d) = (d - c) / (b - a)

P(3.75< x < 4.5)= (4.5 -3.75) / (5 - 3) =0.375

Probability = 0.375