Probability and Statistics Calculations Solved Assignment

This assignment provides detailed solutions to various probability and statistics problems. It includes calculations involving arithmetic operations, fractions, and percentage analysis. Specifically, it covers simplifying mathematical expressions, performing calculations with positive and negative numbers, adding and subtracting fractions, and solving practical problems related to business scenarios such as calculating the number of blue shirts from a total, determining the percentage of students not belonging to the UK, and calculating investment amounts based on given ratios. Furthermore, the assignment includes examples of probability events in the business world and calculates probabilities related to apple selection, bread purchases, and machine product damage. The document also provides statistical analysis, determining mean, mode, median, variance, and standard deviation for a given dataset, offering a comprehensive overview of fundamental statistical and probabilistic concepts. The Desklib platform offers a wide range of similar solved assignments and study resources to aid students in their academic endeavors.

(i) Calculate
a) 850 / (62 + 72) (3*3+3)
Solution
850 / (36 + 49) (12)
850 / (85) (12)
850/1020
= 0.833
b) (4232 / 232 ) (242 / 12)
Solution
(4232 / 529 ) (576 / 12)
(8 ) (48)
=384
c) 1442 / 14 (4 + 4 *4) - 412
Solution
= 1442 / 14 (20) - 412
= 1442 / 280 - 412
= 5.15 – 1681
= - 1675 .85
d) 23 * [ (125 * 5 * 2 + 102) / (5 * 33) ]
Solution
= 8 * [ (1250 + 100) / (135) ]
= 8 * [ (1350) / (135) ]
= 80
e) [726 / (8+3)] / 52 + 8 – 3 + [(52 * 3) 2 ]
Solution
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= [726 / (11)] / 25 + 8 – 3 + [(52 * 3) 2 ]
= [66] / 25 + 8 – 3 + [(52 * 3) 2 ]
= 2.64 + 8 – 3 + [150]
= 157.64
(ii) Calculate
(a) (-33) * (-3)
Solution
= + 99
(b) 41 + (-6)
Solution
= 41 -6
= + 35
(c) (-56) / 7 - (-12)
Solution
= (-56) / 7 + 12
= -8 + 12
= + 4
(iii) Calculate
(a) ¾ + 3/7
Solution
= [ 7*3 + 3*4 ] / 28
= [ 21 + 12 ] / 28
= [ 33 ] / 28
= 1.17
(b) 5/8 - 2/5
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Solution
= [ 5*5 + 2*8 ] / 40
= [ 25 + 16 ] / 40
= [ 41 ] / 40
= 1.025
(c) 16/3 + 12/5
Solution
= [ 16*5 + 12*3 ] / 15
= [ 80 + 36 ] / 15
= [ 116 ] / 15
= 7.73
(iv) Evaluate
a)
Total no of shirts = 65000
Percentage of blue shirts = 42.8%
Solution
Number of blue shirts = [ 65000 * 42.8 ]/ 100
= 27820
Number of blue shirts = 27820
b)
Total no of students = 28000
Percentage of students who belong to UK = 37.6%
Solution
Percentage of students who does not belong to UK = 100 - 37.6 = 62.4%
Percentage of students not belonging to UK = [ 28000 * 62.4 ] /100
= 17472
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v) Calculate
a) Total investment = £180,500
Ratio of investment = 3 : 7 : 5 : 4
Solution
Sum of ratio’s = 3+ 7+5+4 = 19
Investment of A = [ 180500 / 19 ] * 3
= 9500 * 3
Investment of A = 28500
Investment of B = 9500 * 7 = 66500
Investment of C = 9500 * 5 = 47500
Investment of D = 9500 * 4 = 38000
b) Investment of y = £35000
Ratio of investment = 4 : 7 : 3
Solution
7 unit = £35000
So contribution of x = 4 unit = [35000*4 ] /7 = £20,000
Contribution of z = 3 unit = [35000*3 ] /7 = £15,000
Total investment = £35000 + £15,000 + £20,000
= £70,000
(vii) Importance of understanding probability
Business decisions are based on uncertainty. Thus before making any decisions it is vital that one
must understand and accurately analyse the chances of failure as well as success. Such
understanding of probability concepts can help individuals to make more clear decisions on the
basis of expected outcome and future. Hence for growth and ability to reduce failure events and
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improving decision making it is necessary that in business one must have knowledge and
understanding of probability.
PART B
Question 3
(1.)
Total apples = 550
Green = 185
Yellow = 215
Red = 550 – [185 +215] = 150
Probability of choosing green apple = 185/ 550 = 0.33
Probability of yellow apple = 215/ 550 = 0.39
Probability of red apple = 150/ 550 = 0.27
(2.)
Customers buying brown bread = 66%
White bread = 74%
Customers buying both breads = 52%
Solution
Probability of brown bread = 0.66
Probability of white bread = 0.74
Probability of both = 0.52
Probability of at least one bread = 0.66 + 0.74 – 0.52
= 0.88
(3.)
Machine A:
Damage products = 850
Total= 8350
Machine B:
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Damage products = 1030
Total products = 9450
Solution
Probability of getting damage product from machine A = 850/8350 = 0.101
Probability of getting damage product from machine B = 850/8350 = 0.108
Required probability = 0.101 * 0.108 = 0.010
(4.) Examples of probability events
Solution
Three probability events in business world are:
1. When an organisation launches a new product then there are two probabilities, either product
will be successful or it will be a failure.
2. When making an investment decision organisation has two choices. First is that it must invest
and other is it must not invest. Thus to evaluate both these options organisations determine
probability of both possibilities so as to take correct decision.
3. When expanding business to different countries, organisations used to determine the rate of
failure or success in each of the countries. The country which provides max benefit or minimum
risk factor is chosen as the basis for growth or expansion. Thus these probability events are
integral part of business decisions and operations.
Question 4
Days Humidity (x) x - m (x – m)2
1 56 2.4 5.76
2 45 -8.6 73.96
3 48 -5.6 31.36
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4 56 2.4 5.76
5 72 18.4 338.56
6 48 -5.6 31.36
7 45 -8.6 73.96
8 45 -8.6 73.96
9 56 2.4 5.76
10 65 11.4 129.96
Total 536 770.4
Mean m = ∑x / n
∑x = 536 and n = 10
Mean = 53.6
Mode is 45 as it has highest frequency
Median is [ 48 +56 ] / 2 = 52
Variance = ∑ (x – m )2 / n
= 770 .4 / 10 = 77.04
Standard deviation = √ variance
=√77.04 = 8.77
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