**UNIVERSITY EXAMINATIONS: 2012/2013**

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

**IN INFORMATION TECHNOLOGY**

**BIT 1301 PROBABILITY AND STATISTICS**

**DATE: DECEMBER, 2012 TIME: 2 HOURS**

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

**QUESTION ONE**

Twenty five army inductees were given a blood test to determine their blood type. The

data set is as follows:

A B B AB O

O O B AB B

B B O A O

A O O O AB

AB A O B A

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

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

c) A random sample of the life expectancy of residents for 25 countries in Africa

was selected and the following frequency distribution was obtained.

Calculate:

i) The mean

ii) The mode

iii) The median

iv) The standard deviation

v) The 90th and 10th percentile

vi) Coefficient of Skewness and comment

(14 Marks)

d) Three cards are drawn from an ordinary deck and not replaced. Find the

probability of the following.

i) Getting three jacks

ii) Getting an ace, a king and a queen in order

iii) Getting a club, a spade and a heart in order.

iv) Getting three clubs.

(8 Marks)

**QUESTION TWO**

a) A student scored 65 on a calculus test that had a mean of 50 and a standard

deviation of 10, she scored 30 on a history test with a mean of 25 and a standard

deviation of 5. Compare her relative positions on the two tests. (5 Marks)

b) An insurance company researcher conducted a survey on the number of car thefts

in Nairobi for a period of 30 days last month. The raw data are shown below:

52 62 51 50 69 58 77 66 53 57

75 56 55 67 73 79 59 68 65 72

57 51 63 69 75 65 53 78 66 55

Construct a stem and leaf plot by using classes 50-54, 55-59, 60-64, 65-69, 70-74,

and 75-79. (6 Marks)

c) 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:

Gender Yes No

Male 32 18

Female 8 42

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)

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

number of items a person ordered for a large pizza.

Number of

items X

0 1 2 3 4

Probability

P(X)

0.3 0.4 0.2 0.06 0.04

Find the mean of the distribution.

(3 Marks)

**QUESTION THREE**

a) On new year’s eve, the probability of a person driving while intoxicated is 0.32,

the probability of having a driving accident is 0.09, and the probability of a person

having a driving accident while intoxicated is 0.06. What is the probability of a

person driving while intoxicated or having a driving accident. (3 Marks)

b) Five balls numbered 0, 2, 4, 6 and 8 are placed in a bag. After the balls are mixed,

one is selected, it’s number is noted and then it is replaced. If this experiment is

repeated many times, find the variance and standard deviation of the numbers on

the balls. (6 Marks)

c) 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.

(11 Marks)

**QUESTION FOUR**

a) 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)

b) The president of a large university wishes to estimate the average age of the

students presently enrolled. From past studies, the standard deviation is known to

be 2 years. A sample of 50 students is selected and the mean is found to be 23.2

years. Find the 95% confidence interval of the population mean. (6 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.

(8 Marks)

**QUESTION FIVE**

a) A marketing specialist wishes to see whether there’s a difference in the average

time a customer has to wait in a check out line in three large self service

departmental stores. The time in minutes is shown below:

At , is there a significant difference in the mean waiting times of

customers for each store? (8 Marks)

b) 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)

c) Given the data below:

Caalculte

i) The mean of the data

ii) The mode

iii) The median

iv) The standard deviation

(10 Marks)