Oval International
Computer Education
STAT201
1ST SEMESTER FINAL EXAMINATION JUNE 2014
Faculty
:
Science and Technology
Programme
:
Bachelor of Science in Information
Technology
Module
:
Introduction to Statistics
Module Code
:
STAT201
Streams / Groups
:
BSC2
Assessment Type
:
Theory
Date
:
13 June 2014
Time
:
10h00 – 12h00
Duration
:
2 Hours
Maximum Mark
:
100
Examiner
:
Mr I.C Mlitwa
Moderator(s)
:
Internal : Mr J Amod
Instructions to Candidates:
1. Ensure that this examination question paper consists of 4 printed pages and 6 Questions.
2. Answer all questions. Do not use the margins.
3. You may answer the questions in any order, but ensure that ALL sub-questions are kept together.
4. Write legibly and rule-off after each question.
DO NOT TURN THIS PAGE UNTIL PERMISSION IS GRANTED.
2014 1st Semester Final Examinations, Introduction to Statistics 2A (STAT201), Theory
Question 1
a.
Page 2 of 4
[15 Marks]
We wish to chose 7 winners at random to receive prices for a lucky random draw without
replacement(no person can win more than once). There are 52 entries; each person is labeled
number1 to number52. Use the following list of random numbers from left to right to choose the
7 winners:
12651
81769
36737
82861
61646
74436
98863
54371
11769
02630
77240
76610
75109
72310
76251
94934
86993
45049
00654
72748
(10)
b. A city’s telephone book lists 100 000 people. If the telephone is frame for study, how large
would the sample size be if systematic sampling were done on every 200th person.
Question 2
(5)
[15 Marks]
a. Construct a stem and leaf plot using the key 234 = 23|4 for the following data
212
239
240
218
222
249
265
224
257
271
266
239
219
255
260
243
261
249
230
246
263
235
218
238
254
249
250
263
229
221
253
227
270
261
238
240
239
273
220
226
239
258
259
230
255
226
234
229
257
262
(10)
b. From a) above what is the frequency of all data larger than or equal to 250 but less than
270.
(5)
Question 3
[20 Marks]
Complete the following frequency table distribution table and then construct the histogram and
frequency polygon.
(20)
Class Boundaries
Frequency
50.5 – 60.5
13
60.5 – 70.5
27
70.5 – 80.5
43
80.5 – 90.5
31
90.5 – 100.5
9
Midpoint
Relative
frequency
Faculty of Science and Technology, Oval International Computer Education.
Cumulative
frequency
2014 1st Semester Final Examinations, Introduction to Statistics 2A (STAT201), Theory
Question 4
Page 3 of 4
[14 Marks]
4.1 To construct sample spaces for experiments in which we deal with non-numerical data, we
often have to code the various alternatives by assigning them numbers. For instance, if a
mechanic is asked whether work on certain model car is “very easy”, “easy”, “average”,
“difficult” or “very difficult”, we can assign to these alternatives the codes 1, 2, 3, 4 and 5. If A =
{3, 4}, B = {2, 3} and C = {4, 5}, express each of the following symbolically by testing its
elements and describe the event in words.
(a)
(b)
(c)
(d)
A∩B
A B
A∩C
A C
(2)
(2)
(2)
(2)
4.2. From the sample space constructed for the experiment (4)(a) determine
(a)
P(getting a four on the second die)
(2)
(b)
P(getting an even number on both dice)
(2)
(c)
P(sum on the face of both dice exceeds 5)
(2)
Question 5
[13 Marks]
5.1 The probability distribution of X, the number of cylinders to be tuned up in the engines of cars at
a certain service station, is shown below.
X
probability
4
0.5
6
0.3
8
0.2
The cost of tune up for each cylinder is R200. What is the expected tune up cost of
cylinders at this service station?
(3)
5.2. A builder has to choose between two jobs. The first job promises a profit of 80,000 with a
probability of 0.75 or a loss of R25,000 with a probability of 0.25; The second job promises
a profit ofR120,000 with a probability of 0.5 or loss of R45,000 with a probability of 0.5.
Which job should the builder choose if he wants to maximize his expected profit?
(4)
5.3 Given the normally distributed variable X with mean 18 and standard deviation 2.5, find
(a) P(X < 15);
(2)
(b) the value of k such that P(X < k) = 0.2236;
(2)
(c) the value of k such that P(X > k) = 0.1814;
(2)
Faculty of Science and Technology, Oval International Computer Education.
2014 1st Semester Final Examinations, Introduction to Statistics 2A (STAT201), Theory
Question 6
Page 4 of 4
[23 Marks]
6.1 During the last week of the semester, students at a certain university spend on the
average 6.2 hours using the computer terminals with a standard deviation of 1,8 hours.
For a random sample of 36 students at the university, find the probability that the average
time spent during the last week of the semester :
(a) is at least 4,8 hours;
(4)
(b) is between 4,1 and 4,5 hours.
(4)
(c) differs from the actual mean time by no more than 1 hour.
(4)
6.2 Find
(a) F6,20 ; 0.975
(4)
(b) F3,15 ; 0.99
(3)
(c) the value of f such that 5% of the area below the curve is to the right
of it and the numerator degrees of freedom is 7 and the denominator
Maximum Mark: 100
Faculty of Science and Technology, Oval International Computer Education.
Good luck!!!
(4)