A store opens at 8 a.m. From 8 a.m. to 10 a.m. customers arrive at a Poisson rat

Question

A store opens at 8 a.m. From 8 a.m. to 10 a.m. customers arrive at a Poisson rate of four customers per hour. Between 10 a.m. and 2 p.m. their arrival rate increases steadily from four customers per hour to ten customers per hour; and from 2 p.m. to 5 p.m. the arrival rate decreases steadily from ten customers per hour to four customers per hour.

a) Find the probability that at least one customer will arrive before the noon (i.e., 12 o’clock).

b) Find the expected number of customers that will arrive after 1 p.m.

Explanation / Answer

a)probability that at least one customer will arrive before the noon =1-(none will arrive from 8:00 am to 10 am +none will arrive from 10:am to 12 am) =1-(e-4*2+e-10*2)=1-(0.0003+0.0000)=0.9997

b) expected number  of customers that will arrive after 1 p.m=expected customer from 1 pm to 2 pm+expected customer from 2 pm to 5 pm =1*10+3*4=22

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