Statistical Analysis to Support Decision Making
Added on 2023-06-07
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STATISTICAL ANALYSIS TO SUPPORT DECISION MAKING
Student Id/ Name
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Student Id/ Name
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Question 1
a) Cause is a nominal variable since it presents a series of labels which cannot be arranged
in any logical order. If on the other hand, the labels could have been independently
expresses in a logical sequence, then the variable would have been ordinal but this is not
the case here.
b) The appropriate graph is bar chart.
c) Bar chart to represent the data
Vehicle Accident
Fall/slip on same level
Fall from height
Hit by falling object
Pushing/pulling object
Contact with chemical
Cut by tools
Exposed to mental stress
Other mechanisms
0 5 10 15 20 25 30 35
4
25
3
31
5
5
14
4
9
Bar Chart
%
Cause
d) From the above chart, it is apparent that the most common cause of lost-time injury at the
mining site has been through hit by a falling object. Other likely cause of lost-time injuries
include same level fall or slip and also being cut by tools. Together, these three causes
contribute to about 60% of the lost-time injuries incurred at the mining site. The other causes
have relatively low incidence and thus, these major causes must be contained (Lehman &
Romano, 2016).
Question 2
(a) Graphical display of distribution
Mean = 300 grams
1
a) Cause is a nominal variable since it presents a series of labels which cannot be arranged
in any logical order. If on the other hand, the labels could have been independently
expresses in a logical sequence, then the variable would have been ordinal but this is not
the case here.
b) The appropriate graph is bar chart.
c) Bar chart to represent the data
Vehicle Accident
Fall/slip on same level
Fall from height
Hit by falling object
Pushing/pulling object
Contact with chemical
Cut by tools
Exposed to mental stress
Other mechanisms
0 5 10 15 20 25 30 35
4
25
3
31
5
5
14
4
9
Bar Chart
%
Cause
d) From the above chart, it is apparent that the most common cause of lost-time injury at the
mining site has been through hit by a falling object. Other likely cause of lost-time injuries
include same level fall or slip and also being cut by tools. Together, these three causes
contribute to about 60% of the lost-time injuries incurred at the mining site. The other causes
have relatively low incidence and thus, these major causes must be contained (Lehman &
Romano, 2016).
Question 2
(a) Graphical display of distribution
Mean = 300 grams
1
Standard deviation σ =10 grams
(b) Company has the requirement of packets of balls of weight at least 280 grams.
(i) Graph
2
(b) Company has the requirement of packets of balls of weight at least 280 grams.
(i) Graph
2
(ii) The understanding of the empirical rule can be highlighted using the following diagram.
In this case, since μ = 300g and σ = 10g, hence the rejected region would have a probability
of 0.025.
c) 290 g is indicative of μ- σ while 330g is indicative of μ+ 3σ
The % of data lying between μ- 3σ and μ+3σ in accordance with the empirical rule is 99.7%.
However, in order to obtain the answer for the given part, suitable deductions need to be
made for the area between μ- σ and μ- 3σ (Lehman & Romano, 2016).
% values lying between μ- 3σ and μ- σ = 13.5% + 2.5% -[(100-99.7)/2]% = 15.85%
Hence, required probability = 0.997-0.1585 = 0.8385
3
In this case, since μ = 300g and σ = 10g, hence the rejected region would have a probability
of 0.025.
c) 290 g is indicative of μ- σ while 330g is indicative of μ+ 3σ
The % of data lying between μ- 3σ and μ+3σ in accordance with the empirical rule is 99.7%.
However, in order to obtain the answer for the given part, suitable deductions need to be
made for the area between μ- σ and μ- 3σ (Lehman & Romano, 2016).
% values lying between μ- 3σ and μ- σ = 13.5% + 2.5% -[(100-99.7)/2]% = 15.85%
Hence, required probability = 0.997-0.1585 = 0.8385
3
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