Probability An automobile salesman sells cars according to a Poisson process wit

Question

Probability

An automobile salesman sells cars according to a Poisson process with a mean o sold per hour. The salesman works from 8:00 am until 5:00 pm Monday through Saturday The salesman receives the "Big Award" if he sells at least one car on four or more days during a week. f 0.1 cars a. Determine the probability the salesman sells at least two cars on a Tuesday b. the salesman sells exactly one car that Saturday The salesman arrives late (at 10:00 am) on a Saturday. Determine the p During a random week (where the salesman works a full 54-hour week) c. determine the probability the salesman sells no cars before noon Wednesday d. Wednesday at noon, determine the probability the salesman sells no cars the entire week. During a random week, given that the salesman has not sold any cars before Determine the probability the salesman receives the "Big Award" next week. e.

Explanation / Answer

Ans:

Mean=0.1 cars/hr

a)There are 9 working hrs for each day

mean=0.1*9=0.9 cars /day

P(k>=2)=1-P(k<=1)=1-POISSON(1,0.9,TRUE)=1-0.7725=0.2275

b)mean=0.1*7=0.7 cars/day

P(k=1)=POISSON(1,0.7,FALSE)=0.3476

c)9+9+4=22 hrs

mean=0.1*22=2.2 in 22 hrs

P(k=0)=POISSON(0,2.2,FALSE)=0.1108

d)54-22=32 hrs

mean=0.1*32=3.2 in 32 hrs

P(k=0)=POISSON(0,3.2,FALSE)=0.0408

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