**UNIVERSITY EXAMINATIONS: 2013/2014**

**ORDINARY EXAMINATION FOR THE BACHELOR OF SCIENCE **

**IN INFORMATION TECHNOLOGY**

**BIT1301 PROBABILITY AND STATISTICS**

**DATE: APRIL, 2014 TIME: 2 HOURS**

**INSTRUCTIONS: Answer Question ONE and any other TWO**

**QUESTION ONE**

a) The mean mass of a set of components is 750kg and the standard deviation is

50kg. Assuming the masses are normally distributed about the mean, determine

for a sample of 64 components, how many are likely to have masses of.

i. Less than 735kg. (3 Marks)

ii. Between 740 and 760kg. (4 Marks)

b) In a group of40people,10are healthy and every person of the remaining30haseither high blood pressure, a high level of cholesterol or both. If15have highblood pressure and25have high level of cholesterol:

i. How many people have high blood pressure and a high level of

cholesterol? (3 Marks)

ii. If a person is selected randomly from this group, what is the probability

that he or she has high blood

event A . (2 Marks)

iii. If a person is selected randomly from this group, what is the probability

that he or she has high level of cholesterol

event B . (2 Marks)

iv. If a person is selected randomly from this group, what is the probability

that he or she has high blood pressure and high level of

cholesterol

event Aand B . (2 Marks)

v. If a person is selected randomly from this group, what is the probability

that he or she has high blood pressure or high level of

cholesterol

event Aor B . (2 Marks)

vi. Use the above to check the probability formula: (3 Marks)

P AorB P A P B P Aand B .

c) An exploration firm finds that 5% of the test wells it drills yield a deposit of

natural gas. If the firm drills 6 wells, what is the probability that

i. Exactly 2 wells yield gas.

ii. At least 1 well yields gas.

iii. At most 3 wells yield gas.

(6 Marks)

d) The expected number of non-defective bolts in a box is

8

,and the variance is

1.6

.Find the probability that there is only one non-defective bolt in the box.

(3 Marks)

**QUESTION TWO**

a) The table below shows details of monthly salaries and there corresponding

monthly savings for 10 employees. Use it to answer the following questions.

Employee A B C D E F G H J K

Salary (Ksh ‘000’) 20 35 45 15 20 40 32 52 15 25

Savings (Ksh ‘000’) 6 4 8 7 5 9 7 8 5 8

i. Using the least square method, determine the equation of regression line for salary

on income for the data (10 Marks)

ii. A new employee is to be recruited with a monthly salary set at Ksh 30000. Using

the regression line obtained in (i) above, estimated his expected amount of

savings. (2 Marks)

b) A plant produces steel rods whose weights are known to be normally distributed

with the standard deviation of 2.5kg. A random sample of 40 rods had a mean

weight of 33kg.

i. Find the 99% confidence limits for the population mean. (4 Marks)

ii. Find the probability that a steel rod had weight of 35kg or more (4 Marks)

**QUESTION THREE**

a) State three assumptions of a binomial distribution. (3 Marks)

b) Explain the meaning of classification of data. (2 Marks)

c) The following distribution gives the difference in age between husband and wife

in a particular community:

Difference

in age

0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80

Frequency 5 18 33 65 76 69 49 35

Determine the:

i. Arithmetic mean correct two decimal places (4 Marks)

ii. Standard deviation. (5 Marks)

iii. Coefficient of dispersion. (3 Marks)

iv. Third quartile (3 Marks)

**QUESTION FOUR**

a) A department supervisor is considering purchasing a photocopy machine. One

consideration is how often the machine will need repairs. Let

x

denote the

number of repairs during a year. Based on the past performance, the distribution

of

x

is shown as follows.

Number of

repairs ,

x

0 1 2 3

P x 0.2 0.3 0.4 0.1

i. What is the expected number of repairs during a year? (3 Marks)

ii. What is the variance and standard deviation of the number of repairs during a

year? (5 Marks)

b) A committee of

5

people is to be formed randomly from a group of

10

women

and

6

men. Find the probability that the committee has

i.

3

women and

2

men. (3 Marks)

4

ii.

5

women and

1

man. (3 Marks)

iii.

5

women (2 Marks)

iv. At least

3

women. (4 Marks)

**QUESTION FIVE**

a) Define Spearman’s rank correlation co-efficient. (2 Marks)

b) The table below shows the number of crimes committed in sample communities

during a certain period.

Calculate:

i. a rank correlation for the data

ii. Comment on the value in (i) above.

(10 Marks)

c) Between 2 and 4 pm the average number of phone calls per minute coming in to

the switch board of a company is 2.5. Find the probability that during one

particular minute there will be

i. No phone calls at all. (2 Marks)

ii. Exactly 3 calls. (3 Marks)

iii. At least 2 calls. (3 Marks)