**UNIVERSITY EXAMINATIONS: 2017/2018**

**EXAMINATION FOR THE DIPLOMA IN INFORMATION TECHNOLOGY**

**DIT401 PROBABILITY AND STATISTICS**

**FULLTIME/PARTTIME**

**DATE: AUGUST, 2018 TIME: 1 ½ HOURS**

**INSTRUCTIONS: Answer any THREE questions.**

**QUESTION ONE**

a) Find the correlation coefficient by Karl Pearson’s method between x and y and interpret its value

X 57 42 40 33 42 45 42 44 40 56 44 43

Y 10 60 30 41 29 27 27 19 18 19 31 29

(6 Marks)

b) Births in a hospital occur randomly at an average rate of 1.8 births per hour. Determine the

probability of observing 4 births in a given hour at the hospital? (5 Marks)

c) The table below gives the probability distribution of a discrete random variable x.

Given that p(x<13) = 0.75, find the value of k and q hence calculate e(x)

The probability that A hit a target is 1

4

, and the probability that B hits the target is 2/5

Both shoot at the target. Find the probability that:

i) At least one of them hits the target. (3 Marks)

ii) Neither hits the target (2 Marks)

X 4 8 12 15 20

P(x) k 0.25 0.3 q 0.1

**QUESTION TWO**

a) Define the following terms as used in probability

i) Probability (2 Marks)

ii) Independent events (3 Marks)

iii) Dependent events (3 Marks)

b) Discuss any two applications of statistics (2 Marks)

c) You pick one card out of a deck. Determine P (Ace ∪ King). (5 Marks)

d) a certain data set was collected on a random variable x and the following summaries made:

Find the mean and the standard deviation (5 Marks)

**QUESTION THREE**

a) Describe the four properties that qualify an experiment to be described as binomial

(4 Marks)

b) Suppose a die is tossed 5 times. Determine the probability of getting exactly

2 fours (4 Marks)

c) The following is data on the percentage marks obtained by 50 Students in a

Probability and Statistics Exam:

65, 18, 96, 73, 31, 37, 29, 51, 57, 37, 35, 23, 61, 57, 47, 22, 72

15, 12, 46, 53, 78, 68, 23, 40, 47, 50, 74, 87, 63, 63, 42, 43, 61,

81, 8, 38, 43, 59, 76, 13, 59, 56, 43, 51, 56, 21, 67, 45, 53,

i) Prepare a grouped frequency distribution (8 Marks)

ii) Find the mean of the grouped data. (4 Marks)

**QUESTION FOUR**

a) Differentiate between the following terms as used in statistics

i) Qualitative and quantitative variables

ii) Population and sample

iii) Discrete and continuous variables (6 Marks)

b) The total number of goals scored in each football match for 15 matches by a college

team over an year were recorded as follows.

Calculate

i) Mean no. of goals scored (5Marks)

ii) Their Variance and (5 Marks)

iii) Their Standard deviation (4 Marks)

**QUESTION FIVE**

a) Briefly define any THREE measures of central tendency and any THREE measures of

variation (6 Marks)

b) Define the following three methods of data organization

i) Non-frequency data

ii) Ungrouped data

iii) Grouped data (6 Marks)

c) The following grouped data relates to the marks obtained by 27 KCAU Diploma students in a probability

and statistics exam

Determine

i) The mean (2 Marks)

ii) The mode (3 Marks)

iii) The standard deviation (3 Marks)