**UNIVERSITY EXAMINATIONS: 2012/2013**

**FIRST YEAR EXAMINATION FOR THE BACHELOR OF SCIENCE **

**IN INFORMATION TECHNOLOGY**

**BIT 1301 PROBABILITY AND STATISTICS **

**DATE: AUGUST, 2013 TIME: 2 HOURS**

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

**QUESTION ONE**

a) Briefly define the following terms as used in probability and statistics.

i) Sample space

ii) Frequency distribution

iii) Arithmetic mean

iv) Kurtosis

v) Correlation

iv) Mutually exclusive event (6 Marks)

b) Thirty army inductees were given a blood test to determine their blood type. The

data set is as follows:

A B B AB O A

O O B AB B O

B B O A O B

A O O O AB B

AB A O B A AB

Construct a frequency distribution for the data. (2 Marks)

c) i) Using a clearly labeled diagram, show the position of the mean, mode and

median of a positively skewed distribution. (2 Marks)

ii) Given the data set 33, 35, 37, 37, 39, 39, 41, 41, 41, 42, 44, calculate the

mean, median and standard deviation. Hence calculate the first Pearson’s

coefficient of skewness. Comment on the distribution of the data. (7 Marks)

100 students pursuing a course in IT were examined and their results were

summarized as shown in the table below:

Given that the median mark is 47.5. Determine the values of a and b.

(5 Marks)

d) Check the following data set for outliers. 5, 6, 12, 13, 15, 18, 22, 50

(6 Marks)

e) In a hospital unit, there are eight nurses and five physicians. Seven nurses and three

physicians are females. If a staff is selected, find the probability that the subject is a

nurse or a female. (2 Marks)

**QUESTION TWO**

i) a) Two discs are drawn without replacement from a box containing three red and

four white discs. If X is the random variable “the number of white discs

drawn”, find:

i)

E x (6 Marks)

ii)

2 E x (2 Marks)

i)

Var x (2 Marks)

ii)

Calculate

i) The mean of the data

ii) The mode

iii) The median (8 Marks)

**QUESTION THREE**

a) The data obtained in a study of age and systolic blood pressure of six randomly

selected subjects is shown below:

Subject A B C D E F

Age(x) 43 48 56 61 67 70

Pressure(y) 128 120 135 143 141 152

i) Compute the value of the correlation coefficient and comment.

ii) Find the equation of the regression line of y on x.

iii) What is the blood pressure of a 50 year old person? (10 marks)

b) Differentiate between a discrete and a continuous random variable. (2 Marks)

c) A teacher gives a 20 point test to 10 students. The scores are18, 15, 12, 6, 8, 2, 3,

5, 20, 10. Find

i) percentile rank of a score of 12.

ii) the value corresponding to the 25th percentile

iii)the value that corresponds to the 60th percentile. (8Marks)

**QUESTION FOUR**

The masses in grams of 50 small fruits are shown in the following table,

Mass grams Number of Fruits

Calculate the:

a) Mean (2 Marks)

b) Mode (2 Marks)

c) Median (3 Marks)

d) Standard deviation (4 Marks)

e) Interquartile range (3 Marks)

f) First Pearson’s coefficient of skewness (2 Marks)

g) Percentile coefficient of Kurtosis and comment. (4 Marks)

**QUESTION FIVE**

a) A group of computer science students sat probability and statistics and programming

papers in the April 2013 examination. The marks obtained by the candidates were as

follows.

i) Determine the rank correlation coefficient and comment on its value.

(6 Marks)

b) A recent survey asked 100 people if they thought women in the armed forces should

be permitted to participate in combat. The result of the survey are shown in the table:

Find these probabilities:

i) The respondent answered “Yes” given that the respondent was a female

ii) The respondent was a male, given that the respondent answered “No”

(6 marks)

c) In a large restaurant, the following probability distribution was obtained for the

number of items a person ordered for a large pizza.

Find the mean of the distribution. (2 Marks)

d) An exclusive college desires to accept only the top 10% of all graduating seniors

based on the results of a national placement test. This test has a mean of 500 and a

standard deviation of 100. Find the cutoff score for the exam. Assume the variable is

normally distributed. (6 marks)