**UNIVERSITY EXAMINATIONS: 2021/2022**

**SCHOOL OF TECHNOLOGY**

**ORDINARY EXAMINATION FOR THE CERTIFICATE & DIPLOMA IN **

**INFORMATION TECHNOLOGY**

**DIT 107: MATHEMATICS FOR SCIENCE EXAM**

**DATE: DECEMBER 2021 TIME: 2 HOURS**

**INSTRUCTIONS: **

**ANSWER QUESTION ONE (compulsory) AND ANY OTHER TWO**

**QUESTIONS**

**QUESTION ONE (20 MARKS)**

(a) Distinguish between a sample and population. [4 Marks]

(b) Mutually exclusive events and conditional probability [2 Marks]

(c) In a company, a certain computer has 20 folders of which 15 folders contains files with

accounting information and the rest are folders containing files with marketing information 2

folders are selected at random with replacement.

Using a tree diagram, what is the probability that,

(i) They both contain accounting information. [2 Marks]

(ii) One has accounting information while the other contains marketing information.

[3 Marks]

(d) A deck of 52 cards has 13 spades. If two cards are drawn from the deck at random, what is the

probability that both have spades? [3 Marks]

(e) A fair coin is tossed twice. Write down the sample space and find the probability of getting exactly

two heads. [3 Marks]

(f) Highlight THREE features of a good questionnaire as a tool used in data collection.

[3 Marks]

**QUESTION TWO (15 MARKS)**

(a) Solve for x given that

l

(b) Solve for x in the following expression

[2 Marks]

(c) The following data relates to the height of students in a class.

Height (Centimeters). Number of students (Frequency)

150 – 155 3

155 – 160 4

160 – 165 7

165 – 170 9

170 – 175 6

175 – 180 5

180 – 185 4

185 – 190 2

Required:

(i) The mean height of the students [3 Marks]

(ii) The median height of the students [2 Marks]

(iii) Standard deviation and variance of the height of students [3 Marks]

(iv) Coefficient of variation and make a comment [2 Marks]

**QUESTION THREE (15 MARKS)**

(a) Out of a group of 85 people, 30 invested in stock market, 45 had certificates of deposits (CD’s) and

44 had savings bonds. Furthermore, 23 had both CD’s and bonds 13 had CD’s and stocks and 13 had

stocks and bonds. Finally 10 of the people had no investment. Use Venn diagram to determine how

many of the people had

i. All the 3 types of investments. [2 Marks]

ii. At least two investments [2 Marks]

iii. At most two investment [2 Marks]

iv. Savings bonds only [1 Mark]

(b) i. what is a venn diagram? [1 Mark]

i. if A and B are two sets, present their intersection in a venn diagram [1 Mark]

(c) If p, q and r are the propositions

p You get an A on the final exam

**QUESTION FOUR (15 MARKS)**

(a) Using an example in each case, distinguish between a sequence and a series. [2 Marks]

(b) In the following Arithmetic progression, 22,27,32, ……………… determine the 8th term and

10th term. [3 Marks]

(c) Get the sum of the first 7 terms in the following Geometric progression,

4, 12, 36, …………… [2 Marks]