The commuter trains on the Red Line for the Regional Transit Authority (RTA) in Cleveland, OH, have a waiting time during peak rush hour periods of eight minutes ("2012 annual report," 2012).

a.) Find the height of this uniform distribution.

b.) Find the probability of waiting between four and five minutes.

c.) Find the probability of waiting between three and eight minutes.

d.) Find the probability of waiting five minutes exactly.

a) height of this uniform distribution = 1/8 = 0.125.

b) P( 4 < x < 5) = (5 - 4)*0.125 = 0.125

c) P( 3 < x < 8) = (8 - 3)*0.125 = 0.625

d) P(x = 0) = 0*0.125 = 0

Step-by-step explanation:

Height of this uniform distribution is same as finding the probability for each waiting minutes.

Height of uniform distribution = 1/n. Where n is the number of occurence, in this n = 8.

a) height of this uniform distribution = 1/8 = 0.125.

Let random variable x = waiting time.

b) probability of waiting between four and five minutes

P( 4 < x < 5) = (5 - 4)*0.125 = 0.125

c) probability of waiting between three and eight minutes

P( 3 < x < 8) = (8 - 3)*0.125 = 0.625

d) probability of waiting five minutes exactly.

Since this would be just one line, and the width of the line is 0, then the

P(x = 0) = 0*0.125 = 0

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints