HNCB 8 Mathematics for Construction

HNCB 8 MATHEMATICS FOR CONSTRUCTION
By Name
Course
Instructor
Institution
Location
Date

Task 2
Scenario 1
0-4 5-9 10-14 15-19 20-29 30-39
0
5
10
15
20
25
30
35
40
45
0 2 4 6 8 10 12
0
50
100
150
200
250
Revenue
Customers

0-4 5-9 10-14 15-19 20-29 30-39
0
10
20
30
40
50
60
70
80
0 2 4 6 8 10 12
0
2
4
6
8
10
12
Revenue
Customers
(c)
Mean=∑ fx/ ∑ f
=1630.5/144=11.323
Range=5 for the first 4 groups and 1o for the last two groups
Variance σ2 = ∑ fx2
∑ f −x2
= (26652.25/144)-11.3232

56.875
Standard deviation=7.54
Scenario 2
Kolmogorov-Smirnov (K-S) and the Shapiro-Wilk (S-W) tests can be used in the testing of the
assumption that the data sample are extracted from a normally distributed population.
The probabilities provided in the question tend to be cumulative meaning till 1st week, 2nd week
etc. Individual probabilities will be 0.10 in week 1, 0.15 (0.25-0.10) in week two etc.
Individual Failures/week = Total Quantity / Mean Life = 1000 / 3.45 = 289.9
Individual Cost of Replacement = (Individual Failures @ week) x (Individual cost of
replacement) (Kilbas, Srivastava and Trujillo, 2006)
= 289.90 x 3.0 = Rs. 869.60
In week 1: 10 % (0.10) of bulbs would fail out of 1000 bulbs meaning 100
In week 2: 15% of bulbs would fail out of 1000 bulbs meaning 150. Still, 10% of 100 replaced
in week 1 meaning 10 CUMULATIVE bulbs failed by the end of week 2 = 160 (150+10)
Thus, replacing all the bulbs at the same time at fixed interval as well as substituting individual
bulbs which fail in between would turn out to economical or optimal by the end of week 4
(Hyland, 2008).
[N/B: "Yes we can, if..." One of the ways of aiding in obtaining a solution to a [problem of
this type is to respond in the affirmative "Yes we can, if..." For this scenario, the interrogative is,
"Can a conclusion be made that the population mean age is not 30?" Answer, "Yes we can,
should it be possible to eject the null hypothesis indicating that it’s 30." Giving a response to the
challenges in a similar manner all times would result in less confusion as well as limited errors. ]
(I) Data