**UNIVERSITY EXAMINATIONS: 2017/2018**

**EXAMINATION FOR THE DIPLOMA IN INFORMATION **

**TECHNOLOGY**

**DIT401 PROBABILITY AND STATISTICS**

**FULLTIME/PARTTIME**

**DATE: APRIL, 2018 TIME: 1 ½ HOURS**

**INSTRUCTIONS: Answer any THREE questions.**

**QUESTION ONE**

a) The probability that an entering college student will graduate is 0.4. Determine the

probability that out of 5 students

i. None will graduate (3 Marks)

ii. One students will graduate (3 Marks)

iii. At least one will graduate (3 Marks)

iv. All students will graduate (3 Marks)

b) The following is data on the heights of seedlings in a certain tree nursery

3.1 5.1 3.7 4.1 6.8 5.0 3.2 6.0 5.3 4.5 6.4 5.4

5.3 8.3 5.2 5.5 7.3 6.5 6.6 7.5 5.7 5.9 4.8 7.0

7.1 4.0 6.3 4.7 4.8 3.6

Prepare a grouped frequency distribution and find the mean of the

grouped data (8 Marks)

**QUESTION TWO**

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

(4 Marks)

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

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

d) The probability that i 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)

e) The probability that a student owns a computer is 0.65 and the probability that a

student owns a phone is 0.82. If the probability that a student owns both is 0.55. What

is the probability that a given student owns either a phone or a computer (3 Marks)

**QUESTION THREE**

a) The weight of 8 diploma students were taken in variable x as they reported and the

following results calculated.

i. Calculate the mean and the standard deviation of x (3 Marks)

ii. The mean and standard deviation of x after two more students weighing 58kg

and 60 kg respectively join the group (3 Marks)

iii. The mean and the standard deviation of x after each of the 8 students had lost

2kg. (3 Marks)

b) A class has 10 boys and 5 girls, three students are selected at random. Using tree

diagram find the probability that.

(i) All are girls (3 Marks)

(ii) First 2 are boys (3 Marks)

(iii)First and third are of the same sex and the second of opposite sex(5 Marks)

X 4 8 12 15 20

P(x) k 0.25 0.3 q 0.1

**QUESTION FOUR**

a) In a study of the daily production of a company over 50 days, the following data was

corrected

i. Starting with a class 20-29, group this data into a frequency distribution. (5 Marks)

ii. using a suitable assumed mean, calculate the mean and standard

deviation of this data. (6 Marks)

b) in a bag of 40 vegetables, 25 are carrots and 15 are potatoes. The mean weight of the

carrots is 60grams while that of the potatoes is 52 grams. The standard deviations of the

weights are 4 grams and 6 grams for the carrots and potatoes, respectively. Calculate the

mean and standard deviation of all the vegetables in the bag. (6 Marks)

c) In a large flower farm, 20% of a particular kind of flower is red, while all the rest are

white. The farmer decided to take a sample of three flowers from his farm. The third

flower that he picked was white. By use of a tree diagram, find the probability that the

first two flowers he picked were red, given that the third flower is white. Assume

picking with replacement. (3 Marks)

**QUESTION FIVE**

a) Differentiate between the following terms as used in statistics

i. Qualitative and quantitative variables (2 Marks)

ii. Population and sample (2 Marks)

iii. Discrete and continuous variables (2 Marks)

b) The numbers of points scored in each game by a college team were recorded as

follows.

Calculate

i. Mean (3 Marks)

ii. Variance (3 Marks)

iii. Standard deviation (3Marks)

c) A certain data set was collected on a random variable x and the following summaries

made:

i. Find the mean and the standard deviation (3 Marks)

ii. Write down the answers to (i) if ‘10’ is subtracted from each of the

original values