Question

A cereal manufacturer has two new brands of cereal which it would like to produce. Because resources are limited, the cereal manufacturer can only afford to produce one of the new brands. A marketing study produced the following probability distributions for the amount of sales for each of the new brands of cereal.

Table A - Cereal A
Sales	P(Sales)
-$150,000	0.2
$200,000	0.3
$300,000	0.3
$400,000	0.2

Table B - Cereal B
Sales	P(Sales)
-$10,000	0.40
$300,000	0.40
$600,000	0.10
$1,000,000	0.10

a. What are the expected sales of each of the new brands of cereal?

b. What is the standard deviation of the sales for each of the brands of cereal?

c. If both of the brands of cereal cost the same amount to produce, which brand of cereal do you think the cereal manufacturer should produce? Explain.

Answer 1

Soln

Cereal A

Sales (X) in $	Probability (P)	P.X	P.X2
-1,50,000	0.2	-30,000	45000,00,000
2,00,000	0.3	60,000	120000,00,000
3,00,000	0.3	90,000	270000,00,000
4,00,000	0.2	80,000	320000,00,000
Total	1	2,00,000	755000,00,000

Cereal B

Sales (X) in $	Probability (P)	P.X	P.X2
-10,000	0.4	-4,000	400,00,000
3,00,000	0.4	1,20,000	360000,00,000
6,00,000	0.1	60,000	360000,00,000
10,00,000	0.1	1,00,000	1000000,00,000
Total	1	276000	1720400,00,000

a)

Cereal A

Expected Value = ∑P.X = 2,00,000 $

Cereal B

Expected Value = ∑P.X = 2,76,000 $

b)

Cereal A

Std Dev = (∑P.X² - (∑P.X)²)^1/2 = 1,88,414 $

Cereal B

Std Dev = (∑P.X² - (∑P.X)²)^1/2 = 1,88,414 $

c)

Since the Std Dev for Cereal A is less, hence manufacturer should product Cereal A