Question: in general people do not like to wait in a...
In general, people do not like to wait in a queue to be served. At the same time, store owners do not
like their cashiers having no customers. It is a fine balance for store owners to determine how many
employers they roster to work; they want to provide an excellent service to customers but need to be
careful how much money they spend on staff salaries.
Janis is the manager of a small supermarket in her local
town. For a number of consecutive days, Janis observes
the queues at exactly 5 p.m. and then determines the mean
number of customers waiting in line across each of the
open checkouts. Her data is shown:
Mean number of customers
in a queue at 5 p.m. / (Frequency)
Customers: 0 / Frequency: 1
Customers: 1 / Frequency: 12
Customers: 2 / Frequency: 26
Customers: 3 / Frequency: 8
Customers: 4 / Frequency: 3
Janis is interested to understand how long her checkout
queues are, particularly at the peak time of 5 p.m. on
a How many days did Janis observe the queues at 5 p.m.?
b What was the mean, median and mode number of customers in the queue over the observed days?
c Determine the observed probabilities for the number of customers in a queue at 5 p.m.
d What is the probability at 5 p.m. that there will be on average two or more people in the queue?
e If Janis continued her observations for the whole year (365 days), how many times would you expect
there to be 1 person in the queue at 5 p.m.? Give your answer to the nearest whole number of days.