Probability, Research Question, Statistical Decision Making and Quality Control

Running head: ASSIGNMENT 1 1

ASSIGNMENT 1 2
Question 1 Probability
a) Probability is the degree of the likelihood that event will occur. Probability is measured
by taking the ratio of total number of favorable outcome to that of total number of
possible outcome (Roberts, 2018). Probability measure ranges from 0 to 1. This implies
that the likelihood of an event occurs can only lie between 0 and 100%.
b) Given that a compound event composed of the intersection of statistically independent
events, statistical independence of probabilities is the product of the probabilities of its
components (ENCYCLOPÆDIABRITANNICA, 2018).
c)
Sales of Units
(x)
No. of
days p(x)
Exp
value
More
Than
Less
Than [x-E(x)]^2
[x-
E(x)]^2p(x)
0 5 0.05 0 0.95 0 0 0
1 15 0.15 0.15 0.8 0.05 0.7225 0.108375
2 20 0.2 0.4 0.6 0.2 2.56 0.512
3 25 0.25 0.75 0.35 0.4 5.0625 1.265625
4 20 0.2 0.8 0.15 0.65 10.24 2.048
5 15 0.15 0.75 0 0.85 18.0625 2.709375
Total 100 1 2.85 Variance 6.643375
Standard
Deviation 2.577474539
Sales of
Units (x)
No. of
days
p(x) Exp
value
More Than Less Than [x-E(x)]^2 [x-
E(x)]^2p(

ASSIGNMENT 1 3
x)
0 5 =5/B8 =A2*C2
=C3+C4+C5+
C6+C7 0 =(A2-D2)^2 =G2*C2
1 15 =15/B8 =A3*C3
=C4+C5+C6+
C7 =C2 =(A3-D3)^2 =G3*C3
2 20 =B4/B8 =A4*C4 =C5+C6+C7 =C2+C3 =(A4-D4)^2 =G4*C4
3 25 =B5/B8 =A5*C5 =C6+C7 =C2+C3+C4 =(A5-D5)^2 =G5*C5
4 20 =B6/B8 =A6*C6 =C7
=C2+C3+C4+
C5 =(A6-D6)^2 =G6*C6
5 15 =B7/B8 =A7*C7 0
=C2+C3+C4+
C5+C6 =(A7-D7)^2 =G7*C7
Total 100
=SUM(C
2:C7)
=SUM(D
2:D7) Variance
=SUM(H
2:H7)
Standard
Deviation
=SQRT(H
8)
1. 2.85
2. 0.8
3. 0.2
4. 6.643375
5. 2.577474539
d)
1. P ( X >5500 ) =1−Pr (Z ≤ 5500−4700
500 )=0.05 5
2. P ( X > 4500 ) =1−Pr ( Z ≤ 4500−4700
500 )=0.655
3. P ( X < 4900 )=Pr (Z< 4900−4700
500 )=0.655
4. P ( X < 4300 ) =Pr ( Z< 4300−4700
500 ) =0.212
QUESTION 2 Research Question, Constructing data table and calculating probabilities
1. Searched