1.At a road section, an average of 15 vehicles arrive during a10-minute interval. If vehicles arrive according to a Poissondistribution, what is the probability that the number of vehiclesÂarriving 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 timeheadways between successive vehicles are exponentially distributedand that 65% of the headways are greater than 3 seconds. What isthe probability that less than two vehicles arrive during a20-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 hasbeen proposed. During certain periods of the day, significantnumbers of large trucks are expected to depart the terminal’sone-lane driveway to access an interstate highway. Developers wouldlike to know if there are an adequate number of time gaps(headways) in the highway traffic to permit about 40 trucks perhour to enter the highway without the need for a traffic signal. Topermit a truck to safely enter the highway, a time gap of at least8 seconds is needed. Assuming that there will be a flow of 850vehicles on the highway during a design hour, how many gaps oropportunities will there be during the design hour for trucks toenter the highway without a traffic signal? Assume that vehiclearrivals follow a Poisson distribution.
a.849
b.425
c.340
d.212
e.128
