he commuter trains on the Red Line for the Regional Transit Authority (RTA) in Cleveland, OH,...

he 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 exactl

Solutions

Expert Solution

Part a

We are given that waiting periods during peak rush follows uniform distribution.

Waiting time during peak rush hour = 8 minutes

Distance = b – a = 8

Height of uniform distribution = h = 1 / (b – a) = 1/8 = 0.125

Part b

Here, we have to find the probability of waiting between four and five minutes.

We have to find P(4<X<5)

We are given b = 5, a = 4, so b – a = 5 – 4 = 1

Required probability = h*(b – a) = 0.125*1 = 0.125

Part c

Here, we have to find the probability of waiting between three and eight minutes.

We have to find P(3<X<8)

We are given b = 8, a = 3, so b – a = 8 – 3 = 5

Required probability = h*(b – a) = 0.125*5 = 0.625

Part d

Here, we have to find probability of waiting time of exact five minutes.

That is, we have to find P(X=5)

We know that uniform distribution is a continuous distribution and probability for any continuous distribution at particular or exact point is always zero.

So, P(X=5) = 0

Required probability = 0.00

orchestra answered 1 year ago

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