Question

shoppers enter Hamilton place Mall at an average of 120 per hour.
what is the probability that exactly 5 shoppers will enty the mall between noon and 12:05?
what is the probability that at least 35 shoppers will enter the mall between 5:00 and 5:10?

Answer 1

a) The average number of arrivals is given to be 120 per hour, therefore the average number of arrivals in 5 minutes would be given as: 120/12 = 10 arrivals.

Therefore the distribution given here is:

The probability is thus computed here as:

b) For 10 minutes, the average number of arrivals is given as: 120/6 = 20

Therefore, the number of arrivals here could be modelled as:

The probability here is computed as:

This is computed using EXCEL function as:

=1-poisson.dist(34,20,TRUE)

The output here is 0.0015

Therefore 0.0015 is the required probability here.