Question

The truck traffic on a certain highway can be described as a Poisson process with a mean arrival rate of 1 truck per minute. The weight of each truck is random and the probability that a truck is overloaded is 15% 43 What is the probability that there will be at least 2 trucks passing the weight station in a 10 min period Whr the eohubilior bweiehing station will overloaded? Suppose the weighing station will close for 30 min during the lunch hour. What is the probability of overloaded trucks passing the station during the lunch break? Hint: e" = fL y- r!

Answer 1

Ans:

a)

mean=1 truck per min

=10 trucks per 10 min

P(k>=2)=1-P(k<=1)=1-POISSON(1,10,TRUE)=0.9995

b)p=probability of overloaded=0.15

P(k<=1)=BINOMDIST(1,10,0.15,TRUE)=0.5443

c)mean=30 trucks per 30 min

number of overloaded trucks=0.15*30=4.5 i.e 5

P(k=25)=POISSON(25,30,false)=0.05

So,probabaility of overloaded trucks=1-0.05=0.95