# Question: in general people do not like to wait in a...

###### Question details

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:

Table:

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

weekdays.

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.