UNIVERSITY EXAMINATIONS: 2019/2020
ORDINARY EXAMINATION FOR BACHELOR OF SCIENCE
INFORMATION TECHNOLOGY, BSc. APPLIED COMPUTING, BSD,
BISF
BIT 1301/ BUSS 202/ BSD 1203/ BISF 1202/ BAC 1202: PROBABILITY AND
STATISTICS
(DAY/EVENING/DISTANCE LEARNING)
DATE: MAY, 2020 TIME: 6 HOURS
INSTRUCTIONS: Answer ALL Questions
SECTION B
QUESTION ONE (20 MARKS)
(a) Suppose that the total pre-tax profit of IT companies in region ABC is known to be normal
with mean Ksh. 100 million and a standard deviation of Ksh. 80million.Determine
(i) The probability that one of these companies has a pre-tax profit of at most 200million.
(ii) The probability that one of these companies has a pre-tax profit of at least 70 million.
(iii)The number of companies out of 50 that will have a pre-tax of at least 110million.
(10 Marks)
(b) The median and the mode of the following distribution are known to be 27 and 26
respectively.
(i) Show that the values of a and b are 8 and 7 respectively. (5 Marks)
(ii) Compute the arithmetic mean and the standard deviation of the distribution.(5 Marks)
SECTION C
QUESTION TWO (20 MARKS)
(a) Define the following terms as used in probability.
(i) Independent events.
(ii) Conditional probability.
(iii) Outcome.
(iv) Event. [4 Marks]
(b) Ninety students will graduate from Alpha High School this year. Out of the 90 graduates, 50
are planning to attend college. Two students are selected at random to carry the flag at
graduation. What is the probability that both of them are planning to attend college?
[4 Marks]
(c) The information below is the number of daily emergency service calls made by the volunteer
ambulance service of Walterboro, South Carolina, for the last 50 days. To explain, there were
22 days on which there were two emergency calls, and 9 days on which there were three
emergency calls.
(i) Convert this information on the number of calls to a probability distribution. [2 Marks]
(ii) What is the mean number of emergency calls per day? [2 Marks]
(iii)What is the standard deviation of the number of calls made daily? [2 Marks]
(iv)) A and B are two events such that
