Mathematics Online Exam: Statistical Analysis and Probability Concepts

This document presents the solutions to a mathematics online exam, encompassing statistical analysis, probability, and forecasting techniques. Part A includes calculations involving arithmetic operations, percentages, and ratios, along with a discussion on the importance of probability in business decision-making. Part B focuses on statistical measures such as arithmetic mean, mode, median, range, and standard deviation, applied to a humidity dataset. Furthermore, it provides explanations on the significance of statistics, sampling, and forecasting in the business context, illustrating how these concepts aid in decision-making, resource allocation, and risk management. The document offers a comprehensive overview of statistical and probabilistic concepts applied to practical scenarios.

Mathematics online exam

Table of Contents
PART-A...........................................................................................................................................3
I....................................................................................................................................................3
II...................................................................................................................................................3
III.................................................................................................................................................4
IV.................................................................................................................................................5
V..................................................................................................................................................5
VI.................................................................................................................................................6
PART-B...........................................................................................................................................6
QUESTION-4..................................................................................................................................6
QUESTION-5..................................................................................................................................8
I....................................................................................................................................................8
II...................................................................................................................................................8
III.................................................................................................................................................8

PART-A
I
a) 850/ (6²+7²) (3*3+3)
= 850/(36+49) (12)
= 850/1020
= 0.833
b) (4232/23²) (24²/12)
= (4232/529) (576/12)
= (8) (48)
= 384
c) 1442/14 (4+4*4)-41²
= 1442/14(20)-41²
= 1442/280-41²
= 5.15-1681
= -1675.85
d) 2³*[(125*5*2+10²)/(5*3³)]
= 8* [(1250+100)/(135)]
= 8* [(1350)/(135)]
=80
e) [726/(8+3)]/5²+8-3+[(5²*3)2]
= [726/ (11)]/25+8-3+ [(5²*3)2]
= [66]/25+8-3+ [(5²*3)2]
= 2.64+8-3+ [150]
= 157.64
II
a) (-33)*(-3)

= +99
b) 41+(-6)
= 41-6
= +35
c) (-56)/7- (-12)
= (-56)/7+12
= -8+12
= +4
III
a) ¾ + 3/7
= [7*3+3*4]/28
= [21+12]/28
= [33]/28
= 1.17
b) 5/8-2/5
= [5*5+2*8]/40
= [25+16]/40
= [41]/40
= 1.025
c) 16/3+12/5
= [16*5+12*3]15
= [80+36]/15
= [116]/15
= 7.73

IV
a) number of blue shirt: 42.8% of 65000
= 65000*42.8/100
= 650*42.8
= 27820
b) The student who are not from UK:
= number of student from UK: 37.6% of 28000
= 28000*37.6/100
= 280*37.6
= 10528
The student who are not from UK: total student- number of student from UK
= 28000-10528
= 17472
V
a) Investment contributed by each investor: 3:7:5:4 of £ 180500 i.e.
A= 3/19*180500
= £ 28500
B= 7/19*180500
= £ 66500
C= 5/19*180500
= £ 47500
D= 4/19*180500
= £ 38000
b) investment made by X and Z and sum of total investment
Y share: 7/14=35000
From hit and trial method it can be calculated that if 7/14=35000 which means the total sum
would be 70000 i.e. 70000*7/14=35000
Hence, the total sum will be 70000

X share: 4/14*70000
= 20000
Z share: 3/14*70000
= 15000
VI
As the business world involve the high percentage of risk as well as uncertainties in terms of
occurring of such situation which may negatively impact the company and its business so here
ascertainment of probability plays an important role. This is because with the situation of
probability the business can determine the chances of success. In the same way with the aspect of
probability the business can make decision in terms of its future policies and plans because the
probability enable the business to have sufficient proportion of assurance regarding the possible
outcome. In the same way the with the concept of probability towards the various perspective say
with respect to investment and making an analysis regarding the return would be made easily
performed with the concept of probability. Through probability the uncertainties as well as
changing situation of the business would be able to identified and analysed that will lead to assist
the business in bearing uncertainties and attain success.
PART-B
QUESTION-4
a) Arithmetic mean:
Mean= Sum of terms/ number of terms
= 56+45+48+56+72+48+45+45+56+68/10
= 53.9
b) The Mode: It is most repetitive number
= 56 and 45 because they occur maximum times
c) The median:
step:1 arrangement of number in ascending order
45,45,45,48,48,56,56,56,68,72
Step:2 find the middle two number

= 48,56
Step:3 add the two number and divide by 2
=48+56/2
= 52
d) The range:
Highest number-lowest number
= 72-45
= 27
e) The standard deviation:
Days Humidity X-m (x-m2)
1 56 2.1 4.41
2 45 -8.9 79.21
3 48 -5.9 34.81
4 56 2.1 4.41
5 72 18.1 327.61
6 48 -5.9 34.81
7 45 -8.9 79.21
8 45 -8.9 79.21
9 56 2.1 4.41
10 65 11.1 123.21
total 536 771.3
= 771.3/10-1
= 771.3/9
= 85.7
Standard deviation: √85.7
= 9.25

QUESTION-5
I
Statistics can be defined as which is concerned with the development and studying of
methods that include collection, analysis, interpretation along with presentation of empirical
data. it can also be defined as a collection of quantitative data that would include the calculation
with numerical facts and figures so that the interpretation can be made accordingly. In other
words, statistics can also be defined as discipline under which the collection, organization,
analysis, interpretation as well as presentation of data will be made. The example of statistics
includes the reports of government or the quantitative data like a report of number which say
how many followers of each religion are there in a country. With this report it can be analysed
the number of people of particular religion in the country so that policies can be framed
accordingly.
II
Sampling plays an important role in respect to business world because with the mode of
sampling the business decision can be taken easily. This is because sampling enable quick
decision making as under sampling it is assumed that the chosen sample will show and depict all
the characteristics which the entire population present. This means with the mode of sampling
the business decision as well as analysis can be made performed in an easy manner. This can be
justified with an example i.e. with the use of sampling say taking the sample of customers from
the market will assist the business in terms of taking decision towards its product. This means
with a sample of its customer the company can frame its future planning towards its product
along with making an improvisation of its existing product.
III
Forecasting plays an important role in the business because with the mode of forecasting the
business can depict the estimated cost as well as expenses. The forecasting will also enable the
business to estimate the profit too. Likewise, with the mode of forecasting the business can
determine its future course of action. Forecasting will lead to assist the business in terms of
framing of strategies towards the success of the business. With the help of forecasting of
estimated expenses, the company can make frame concerned policies so that the expenses can be

controlled. In the same way with the help of forecasting the future profit the company can make
determine that whether its business will prove to be successful in the market or not. This means
forecasting proves to be highly important in respect to taking of business decision as well as
controlling towards expenses. With the mode of forecasting the future plans and policies can also
be made by the business that will entitle profit and success to the companies.

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