Decision Making - Study Material with Solved Assignments

This study material covers topics such as probability, statistical independence, direct labor time, and more. It includes solved assignments, essays, and dissertations. The data for age and sex for the Australian population is collected from the website of Australian bureau of Statistics. The table 3235.0 Population by Age and Sex, Regions of Australia has been taken. The data estimates the population on 30th June 2016.

Running Head: DECISION MAKING
Decision Making
Name of the Student
Name of the University
Author Note

1DECISION MAKING
Table of Contents
Answer 1..........................................................................................................................................3
Part a............................................................................................................................................3
Part b............................................................................................................................................3
Part c............................................................................................................................................3
Part 1............................................................................................................................................3
Part 2............................................................................................................................................3
Part 3............................................................................................................................................4
Part 4............................................................................................................................................4
Part 5............................................................................................................................................4
Part 6............................................................................................................................................4
Part d............................................................................................................................................4
Part 1............................................................................................................................................4
Part 2............................................................................................................................................4
Part 3............................................................................................................................................5
Part 4............................................................................................................................................5
Answer 2..........................................................................................................................................5
Part 1............................................................................................................................................5
Part 2............................................................................................................................................5
Part 3............................................................................................................................................6

2DECISION MAKING
Part i.............................................................................................................................................6
Part ii............................................................................................................................................6
Part iii...........................................................................................................................................6
Part iv...........................................................................................................................................6
Answer 3..........................................................................................................................................6
Part a............................................................................................................................................6
Part 1............................................................................................................................................6
Part 2............................................................................................................................................7
Part 3............................................................................................................................................7
Situation 1....................................................................................................................................7
Situation 2....................................................................................................................................7
Situation 3....................................................................................................................................8
Part b............................................................................................................................................8
Reference.......................................................................................................................................10

3DECISION MAKING
Answer 1
Part a
Probability can be defined as the ratio of an outcome to the total number of outcomes.
It is measured as ratio.
Probability can take all values between 0 and 1.
Part b
The condition when the existence of an event or outcome does not in any way affect the
existence of another event or outcome is known as statistical independence.
Statistical independence is identified by testing for the independent occurrence of two events.
Part c
Part 1
Sales
Units
(x)
No.
of
days
p(x) Exp value More
than
Les
than [x-E(x)]2 [x-E(x)]2 p
(x)
0 5 0.05 0 100 5 0.000 0.000
1 15 0.15 0.15 95 20 0.723 0.108
2 20 0.2 0.4 80 40 2.560 0.512
3 25 0.25 0.75 60 65 5.063 1.266
4 20 0.2 0.8 35 85 10.240 2.048
5 15 0.15 0.75 15 100 18.063 2.709
Total 100 1 2.85 Varianc
e 6.643
Standard
Deviation 2.577
Part 2
The average daily sales = 2.85

4DECISION MAKING
Part 3
The probability of selling 2 or more than 2 loaves ¿ 80
100 =0.8
Part 4
The probability of selling 2 or less than 2 loaves ¿ 40
100 =0.4
Part 5
The variance of the distribution = 6.643
Part 6
The standard deviation of the distribution = 2.577
Part d
Part 1
The probability of sales being greater than 5500 oranges –
P ( Z >5500 ) =P (Z > X −μ
σ )
( 4700−5500 )
500 =−800
500 =−1.6
P ( Z >−1.6 )=0.0548
Part 2
The probability of sales being greater than 4500 oranges –
P ( Z > 4 500 )=P( Z > X−μ
σ )
( 4700−4 500 )
500 = 2 00
500 =0.4

5DECISION MAKING
P ( Z >0.4 )=.6554
Part 3
The probability of sales being less than 4900 oranges –
P ( Z <4 9 00 )=P (Z < X−μ
σ )
( 4700−4 900 )
500 =−200
500 =−0.4
P ( Z ←0.4 )=1−0.3446=0.6554
Part 4
The probability of sales being greater than 4300 oranges –
P ( Z < 4 3 00 ) =P(Z < X−μ
σ )
( 4700−4 3 00 )
500 = 200
500 =0.4
P ( Z <0.4 ) =1−.6554=0.3446
Answer 2
Part 1
The data for age and sex for the Australian population is collected from the website of
Australian bureau of Statistics. The table 3235.0 Population by Age and Sex, Regions of
Australia has been taken. The data estimates the population on 30th June 2016.
Part 2
Age Range Males Females Total
0 – 14 3948119 3455472 7403591
15 – 24 2733951 2424155 5158106

6DECISION MAKING
25 – 54 8351616 7844279 16195895
55 – 64 2285207 2200309 4485516
65 and over 2865407 3028986 5894393
Total 20184300 18953201 39137501
 http://www.abs.gov.au/AUSSTATS/abs@.nsf/DetailsPage/3235.02016?
OpenDocument#Data
Part 3
Part i
The probability that a randomly selected person is a female ¿ 18953201
39137501=0.48
Part ii
The probability that a randomly selected person is in the age range of 25 – 54 ¿ 16195895
39137501=0.41
Part iii
The joint probability that a randomly selected person is a male and in the age range of 55 to 64
¿ 2285207
39137501=0.06
Part iv
The conditional probability that a person is between the age of 25 and 64 and is a female
¿ 10044588
18953201=0.53
Answer 3
Part a
Part 1
Direct labour time has a mean of (X ) 30 hours
The standard deviation of direct labour time is (σ ) 10 hours

7DECISION MAKING
The number of samples taken (n) is 64
The control limits are calculated as X ± z α
2
∗
( σ
√n )=30 ± 1.96∗10
√64
At 95% confidence interval z α
2
=1.96
Hence, the LCL for direct labour time = 27.55 hours
Hence, the UCL for direct labour time = 32.45 hours
Part 2
When sample size = 16
The control limits are X ± z α
2
∗
( σ
√ n ) =30 ± 1.96∗10
√ 16
Thus, the LCL for direct labour time = 22.6 hours
Thus, the UCL for direct labour time = 37.4 hours
Part 3
Situation 1
The confidence interval is changed to 90%.
At 90% confidence interval z α
2
=1.645
Thus, at 90% confidence interval and sample size of 16
The control limits are X ± z α
2
∗
( σ
√ n ) =30 ± 1.645∗10
√ 16
Thus, the LCL for direct labour time = 25.89 hours
Thus, the UCL for direct labour time = 34.11 hours
Situation 2
When sample size is 64 and confidence interval is 95%, then

8DECISION MAKING
The LCL for direct labour time = 27.55 hours
The UCL for direct labour time = 32.45 hours
Situation 3
When sample size is 36 and confidence interval is 95%, then
The control limits are X ± z α
2
∗
( σ
√n )=30 ± 1.96∗10
√36
Thus, the LCL for direct labour time = 26.73 hours
Thus, the UCL for direct labour time = 33.27 hours
From the three situations it is found that for a 95% confidence interval and sample size of 64 has
the narrowest control limit.
Part b
Null Hypothesis: The mean distance to the nearest fire station is 5.5 km
H0 : μ=5.5
Alternate Hypothesis: The mean distance to the nearest fire station is not greater than 5.5 km
H A : μ<5.5
At 63 degrees of freedom and 0.05 level of significance the t-crit value is 1.6694.

9DECISION MAKING
t−stat= 5.8−5.5
2.4
√ 64
=1.0
Since, the t-stat value is less than the t-crit, hence the Null hypothesis is not rejected. Thus the
mean length is equal to 5.5km.

10DECISION MAKING
Reference
Australian Bureau of Statistics, 2016, Population by Age and Sex, Regions of Australia, viewed
04 August 2018,
<http://www.abs.gov.au/AUSSTATS/abs@.nsf/DetailsPage/3235.02016?OpenDocument#Data>