1.At a road section, an average of 15 vehicles arrive during a 10-minute interval. If vehicles...

1.At a road section, an average of 15 vehicles arrive during a 10-minute interval. If vehicles arrive according to a Poisson distribution, what is the probability that the number of vehicles arriving during a 3-minute interval is between 2 and 5 (i.e., 2 ≤ k ≤ 5)?

a.0.110

b.0.171

c.0.642

d.0.653

e.0.703

2.At a specific point on a highway, it is known that the time headways between successive vehicles are exponentially distributed and that 65% of the headways are greater than 3 seconds. What is the probability that less than two vehicles arrive during a 20-second interval?

a.0.219

b.0.233

c.0.350

d.0.397

e.0.412

Construction of a new fright terminal along a rural highway has been proposed. During certain periods of the day, significant numbers of large trucks are expected to depart the terminal’s one-lane driveway to access an interstate highway. Developers would like to know if there are an adequate number of time gaps (headways) in the highway traffic to permit about 40 trucks per hour to enter the highway without the need for a traffic signal. To permit a truck to safely enter the highway, a time gap of at least 8 seconds is needed. Assuming that there will be a flow of 850 vehicles on the highway during a design hour, how many gaps or opportunities will there be during the design hour for trucks to enter the highway without a traffic signal? Assume that vehicle arrivals follow a Poisson distribution.

a.849

b.425

c.340

d.212

e.128

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Ally Wells answered 1 week ago

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