Accounting Decision Support Tools

ACCOUNTING DECISION SUPPORT TOOLS
Student’s Name
Class
Date

2
Question 1
a. Expected value
Expected value is an average return someone can expect from a series of action or
experiment. It measures the expected result when someone do some random experiment or make
a selection from a set of random values.
Expected value is calculated by multiplying the probability of an event occurring by the total
number of occurrences.1 For example, when you have 10 questions of multiple choices of A, B,
C, D and E. When all the choices is C from all the questions, the probability of passing is 0.20.
Therefore, p ( x )=0.20∧occurences is10 then expected value E ( x )=0.20× 10=2.
b. Sales of loaves
1. Tables
Sales
unit
(x)
Number of
days
p(x) Exp
value
E(x)
More
than
Less
than
0 5 0.05 0 0 2.9 0 0
1 10 0.1 0.1 0.1 2.9 0.81 0.081
2 25 0.25 0.5 0.6 2.8 2.25 0.5625
3 25 0.25 0.75 1.35 2.3 5.0625 1.265625
4 20 0.2 0.8 2.15 1.55 10.24 2.048
5 15 0.15 0.75 2.9 0.75 18.0625 2.709375
Total 100 0.85 2.9 7.1 13.2
0.65 Variance 6.6665
Std
deviation
2.581956622
1 Hancock, Volante, and Lau, "Quantifying Qualitative Probabilities,” 155-159.
[ x−E ( x ) ]2
[ x−E ( x ) ]2
p( x )

3
Sales unit (x) Number of days p(x) Exp value E(x) More than Less than
0 5 =B2/B8 =A2*C2 =D2 =D2+D3+D4+D5+D6+D7=(A2-D2)*(A2-D2) =G2*C2
1 15 =B3/B8 =A3*C3 =E2+D3 =F2-D2 =(A3-D3)*(A3-D3) =G3*C3
2 25 =B4/B8 =A4*C4 =E3+D4 =F3-D3 =(A4-D4)*(A4-D4) =G4*C4
3 25 =B5/B8 =A5*C5 =E4+D5 =F4-D4 =(A5-D5)*(A5-D5) =G5*C5
4 20 =B6/B8 =A6*C6 =E5+D6 =F5-D5 =(A6-D6)*(A6-D6) =G6*C6
5 10 =B7/B8 =A7*C7 =E6+D7 =F6-D6 =(A7-D7)*(A7-D7) =G7*C7
Total 100 =C4+C5+C6+C7 =D2+D3+D4+D5+D6+D7=E2+E3+E4+E5+E6+E7=F2+F3+F4+F5+F6+F7
=C5+C4+C3+C2 Variance =H2+H3+H4+H5+H6+H7
Std deviation =SQRT(H9)
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2. The average daily sales is 2.9. The average daily sales is the accumulated expectation of
all the occurrences.
3. Probability of selling two or more loaves 0.85. The probability of selling two or more we
get by adding the individual probability from 2 sales to 5 sales.
4. The probability of selling three or less loaves is 0.65. The probability of selling 3 or less
we get by adding individual probability from 3 sales back to sales 0.
5. Variance of distribution is 6.6665. We get the variance by adding the values in the
column 8
6. Standard deviation 2.5820. The standard deviation is the square root of variance.
c. Four machines
Machine W X Y Z All machines
Grade
Satisfactory 3,200 800 2,400 1,600 8,000
Rework 600 150 450 300 1,500
Scrap 200 50 150 100 500
All grades 4,000 1,000 3,000 2,000 10,000
1. The probability of the part being produced by Machine W and should be reworked when
selected randomly is;
600
10000 = 6
100 =0.06
Here we find 0.06 by taking parts under Machine W and need to be reworked then divide by
the total number of all parts.
2. The probability of the part being produced by Machine Z and is not satisfactory when
randomly selected is;