Statistics and Probability Assignment - Analysis and Solutions

This document presents a comprehensive solution to a statistics and probability assignment. The solution includes detailed calculations and explanations for various statistical concepts. Part A covers calculations involving basic arithmetic operations, and probability, answering questions on calculating values. Part B focuses on descriptive statistics, providing calculations for the mean, mode, median, range, and standard deviation. The assignment also explores fundamental concepts such as data types, population vs. sample, and the normal distribution. The solutions are presented clearly, making it easy to understand the application of statistical methods and the interpretation of results. The assignment offers a practical guide to solving common statistical problems.

PART A
Question 1:
I.
a) 300 ÷ (8 2 + 6 2) (3 × 2 + 2)
= 300 ÷ (100) (8)
= 300 ÷ 800
= 0.375
b) (400 ÷ 202) (625 ÷ 125)
= (1) (5)
= 5
c) 810 ÷ 9 (5 × 5 -5) – 200
= 810 ÷ 9 × 20 – 200
= 90 × 20 – 200
= 1800 – 200
= 1600
d) 2 × [502 ÷ (2 × 54)]
= 2 × [2500 ÷ 1250]
= 2 × 2
= 4
e) [144 ÷ (10 + 8)] ÷ 2 + 10 – 2 + [(52× 2) 2]
= [144 ÷ 18] ÷ 2 + 10 – 2 + [100]
= 8 ÷ 2 + 10 – 2 + 100
= 4 + 10 – 2 + 100
= 112
II.
a) 176
b) 99
c) -1

III.
a) 0.708
b) 0.425
c) 8 3
4
IV.
a) 27,472 green tea bags
b) 5,660 students not based in England
V.
a) A= £40,000
B = £15,000
C = £25,000
D = £20,000
b) X = £30,000; Z = £42,000
Total Investment = £108,000
VI. Probability helps business to analyze the risk and assess the profit accordingly
PART B
Question 4
a) Mean = 74.4
b) Mode = 65
c) Median = 74.5
d) Range = 21
e) Standard Deviation = 7.136
Question 5
I. Data is any value in the form of numeric either in discrete, random or continuous type.

Information is anything which can be interpreted from the data.
II. Population is the inclusion of all data from specified area. Sample is the small portion of
population data which is taken to analyze the whole population within less time and cost. Larger
the sample size more will be chances of error.
III. A normal distribution is the proper term for a probability bell curve. In a normal
distribution the mean is zero and the standard deviation is 1. It has zero skew and a kurtosis of
3. Normal distributions are symmetrical, but not all symmetrical distributions are normal.
Types of skewed data = Positive, Negative and Zero