Question

Your company maintains a database with information on your customers, and you
are interested in analyzing patters observed over the past quarter. 23% of customer
in the database placed new orders within this period. However, for those customers
who had a salesperson assigned to them, the new order rate was 58%. Overall, 14%
of customers within the database had salesperson assigned to them.
a) Draw a contingency table for this situation.
b) What percentage of customers in the database placed a new order but did not
have a salesperson assigned to them.
c) Given that a customer did not place a new order, what is the probability that the
customer had a salesperson assigned to him or her?
d) If a customer did not have a salesperson assigned to him or her, what is the
probability that the customer placed a new order?

Answer 1

Answer (a):

Salesperson assigned (down )	Placed new order ----->	Yes	No	Total
Yes
No
Total			100

Lets assume the total number of customers in the databse are 100.

Now given,

23% of customer in the database placed new orders i.e 23 customers have placed new order (this is the cell yellow in table) i.e total of the yes column (placed new order)

Salesperson assigned (down )	Placed new order ----->	Yes	No	Total
Yes
No
Total	23		100

Given,

14%of customers within the database had salesperson assigned to them. This is the cell red i.e total of Yes row (salesperson assigned).

Salesperson assigned (down )	Placed new order ----->	Yes	No	Total
Yes			14
No
Total	23		100

Given, customers who had a salesperson assigned to them, the new order rate was 58%.

i.e the cell green denotes customers who had a salesperson assigned to them, and placed a new order. This is equal to

58 % of 14 = 8.12

Salesperson assigned (down )	Placed new order ----->	Yes	No	Total(sum)
Yes	8.12		14
No
Total(sum)	23		100

Now we can fill rest of the cells based on the few filled entries in the table.

Salesperson assigned (down )	Placed new order ----->	Yes	No	Total(sum)
Yes	8.12	5.88	14
No	14.88	71.2	86
Total(sum)	23	77	100

Answer (b):

percentage of customers in the database placed a new order but did not
have a salesperson assigned to them. = cell blue = 14.88

Answer (c):

Given that a customer did not place a new order, the probability that the
customer had a salesperson assigned to him or her =

5.88/77 = 0.076

Note that probability is asked here, not the percentage or no of customers.

Answer(d):

If a customer did not have a salesperson assigned to him or her,
the probability that the customer placed a new order =

14.88 / 86 = 0.17

Please let me know if you have any doubts/questions/need more explanation. Thanks