Download University of Nairobi

UNIVERSITY OF NAIROBI
SCHOOL OF BUSINESS
DEPARTMENT OF MANAGEMENT SCIENCE
DMS 501: BUSINESS QUANTITATIVE ANALYSIS
JANUARY TO MAY 2013 SEMESTER
PROBABILITY & STATISTICS ASSIGNMENT
DUE DATE: 8TH APRIL 2013
______________________________________________________________________
Question 1
In a study to analyse performance in a 2012 examination series the following scores in
percentage were compiled for a sample of 100 candidates.
42,51,52,53,61,62,63,64,71,72,81,46,53,54,55,63,64,65,66,73,74,82,48,57,58,59,67,68,
69,77,78,87,43,54,56,64,65,66,67,74,75,84,47,52,53,54,62,63,64,65,72,73,82,45,56,57,
58,66,67,68,69,76,77,86,44,55,56,57,65,66,67,75,76,85,49,50,51,52,60,61,62,70,71,51,
52,53,61,62,63,71,72,58,59,57,68,69,67,78,79,80
a) Arrange the data in equal classes of size 10 starting from 40 percent.
b) Using an ogive for the data, find:
i)
The approximate percentage of the candidates who passed the
examination if the pass mark was 62.5 percent.
ii)
The pass mark if 90 percent of the candidate passed examination.
c) Verify whether it would be appropriate to use the properties of normal probability
distribution in analyzing the data (perform acid test of normality).
Question 2
a) A game of chance entails tossing three coins. For each head that comes up, the
player receives Ksh 1000 and loses Ksh 800 for any tail that comes up. To play
the game, one pays Ksh 1500.
Advise a player whether if is advisable to play the game.
b) Win-Win Consult ltd. bids for 10 jobs, believing that its chances of getting each of
the jobs is 0.1.
i)
What is the probability that it gets at least two of the jobs?
ii)
What is the expected value of the number of jobs it will get?
iii)
What is the standard deviation of the number of jobs it will get?
c) The number of patients entering the intensive care unit of Great Care Hospital
(GCH) on any one day has a Poisson probability distribution with a mean equal
to 5 patient per day.
What is the probability that the number of patient entering the intensive care unit
on a particular day is greater that two.
d) Sweet Unga Ltd. packs wheat flour in packets whose weights are normally
distributed with mean equal to 5kg and standard deviation equal to 0.2 kg. The
company classifies its packets as “under weight” when its weight falls below 4.7
kg; ”over weight” when above 5.1 kg; otherwise it is classified as “normal weight”.
The customers are charged Ksh 1700, 2000 and 2100 for the various packets
respectively.
A customer is supplied with consignment of 1000 packets of the wheat flour. How
much would the customer be expected to pay to the company?
e) A study was conducted to determine student, faculty, and administration
attitudes on a new University parking policy. The distribution of those favouring or
opposing the policy is shown in the following table:
Student
Faculty
Administration
Favour
252
107
43
Oppose
139
81
40
Do the data provide sufficient evidence to indicate that attitudes regarding the
parking policy do not depend on the category of the respondent?
Question 3
For the grouped data in Question 1:
a) Find an interval estimate of the actual average performance in the examination.
b) Suppose the expected average performance in the examination was 72 percent,
would we be right to say that this group of candidates performed below the
average?
c) A sample of 50 scores were obtained from 2011 series of a similar examination.
The sample gave a mean score of 66.7 percent with a standard deviation of 3
percent.
Would we be right to conclude that there was no difference in performance
between 2011 and 2012 series of the examination?
Question 4
Mr. Bookman, a new fiction author, wishes to know whether there is any relationship
between a book’s length and the price charged for the book. He chooses a random
sample of 10 novels and records the length and price of each as follows:
Length (pages)
520 680 740 200 400 800 750
Price (Ksh 00)
16
20
21
9
10
22
20
500 300 350
15
10
10
a) Is there a significant relationship between novel length and its price? (use test for
significance of correlation)
b) Develop a regression model for predicting the price of a novel using its length.
c) Test the significance of the model using t-test, R2 and F-test.