Download Exam1 - Academic Information System (KFUPM AISYS)

1
KING FAHD UNIVERSITY OF PETROLEUM & MINERALS
DEPARTMENT OF MATHEMATICAL SCIENCES
DHAHRAN, SAUDI ARABIA
STAT213 STATISTICS METHODS FOR ACTUARIES
First Mid Term Exam, Term 112
Time:
6:00 p.m. to 7:30 p.m.,
Mar 11 , 2012
Instructors: Hassen Muttlak
Student Surname:
ID#
You are allowed to use electronic calculators and other reasonable writing accessories that
help write the exam. Try to define events, formulate the problem and solve it. See the
example below.
Example Q:
(3pts) Find the Area of a rectangle with perimeter of 30 units and length of 8 units.
Example Answer with grading point scheme.
Perimeter =2(l + w) = 30  l + w = 15
Length = l = 8  w = 15-l = 7
 Area = l*w = 8*7 = 56 unit2.
(1 pt)
(1pt)
(1 pt)
Do not keep your mobile with you during the exam, turn off your mobile and leave it
aside.
Question No
1
Full Marks
16
2
6
3
5
4
5
5
13
Total
45
Marks Obtained
2
Q1. (5+3+3+5)=16
A chemical engineer studied the effect of reflux rate on the yields from a distillation column.
Here are the yields
X
Where
a.
b.
c.
d.
X
90
95
90
95
92
95
92
95
92
95
93
96
94
96
94
97
94
97
94
97
=1882  X =177176
2
Check the empirical rule for the given dataset.
Prepare a frequency distribution of the reflux rates. Use intervals of length 2.
Draw the relative frequency curve of the reflux rates. Comment on the shape of the
curve.
Construct The Box plot. Comment on variability of the data set.
3
Q2. (3+3)=6
The probability that a computer contains a virus is 0.25, and the probability that it has a worm is 0.07.
Also 27% computers have either a virus or a worm.
a.
b.
If somebody scans the computer and finds no virus, what is the probability that the computer
contains a worm?
Are the events ‘having a virus’ and ‘having a worm’ independent? Give a probabilistic
justification.
Q3. (2+3) = 5
A survey of those using a particular statistical software system indicated that 12% were dissatisfied.
Half of those dissatisfied purchased the system from company A. It is also known that 22% of those
surveyed purchased from company A.
a. What is probability of a satisfied customer purchasing the system from company A?
b. Given that the software package was purchased from company A, what is the probability that
a particular user is dissatisfied?
4
Q4. (3+2) = 5
Each of 2 identical cabinets has 2 drawers. Cabinet A contains a silver coin in each drawer, and
cabinet B contains a silver coin in one of its drawers and a gold coin in the other. Suppose that the
selection of cabinets is equally likely.
a. One cabinet is randomly selected; one of its drawers is opened, what is the probability that a
silver coin is found?
b. If a silver coin is found in the first drawer, what is the probability that there is a silver coin in
the other drawer?
Q5. [13 points] Answer the following questions by choosing the right answer.
1. Which of the following statistics is not a measure of central tendency?
a. mean
2.
b. median
c. mode
d. Q3
In a perfectly symmetrical bell-shaped "normal" distribution
a.
b.
c.
d.
the mean equals the median.
the median equals the mode.
the mean equals the mode.
all of these
3. The smaller the spread of scores around the arithmetic mean
a.
b.
c.
d.
the smaller the interquartile range.
the smaller the standard deviation.
the smaller the coefficient of variation.
all of these.
5
4. The set of all possible outcomes from a random experiment is called the:
a. sample population.
b. sample space.
c. sample probability.
d. sample event.
5. If the probability of occurrence of event A is not affected by the occurrence of event B, then A and
B are said to be:
a.
b.
c.
d.
6.
Which of the following is the appropriate definition for the union of two events A and B?
a.
b.
c.
d.
7.
mutually exclusive
statistically independent
collectively exhaustive
basic events
The set of all basic outcomes contained within both A and B.
The set of all basic outcomes in either A or B, or both.
The set of all possible outcomes.
None of these.
If you are interested in comparing variation in sales for small and large stores selling different
goods, which of the following is the most appropriate measure of dispersion?
a. The range
b. The interquartile range
c. The standard deviation
d. The coefficient of variation
8. A type of vertical bar chart in which the categories are plotted in the descending rank order of the
magnitude of their frequencies is called a:
a. contingency table.
b. Pareto diagram.
c. dot plot.
d. pie chart.
9. Suppose you are told that the mean sample of numbers is below the median. What does this
information suggest?
a.
b.
c.
d.
The distribution is symmetric.
The distribution is skewed to the right or positively skewed.
The distribution is skewed to the left or negatively skewed.
There is insufficient information to determine the shape of the distribution.
10. The width of each bar in a histogram corresponds to the
a.
b.
c.
d.
differences between the boundaries of the class.
number of observations in each class.
midpoint of each class.
percentage of observations in each class.
6
11. What is the relationship among the mean, median and mode in a positively skewed distribution?
a. The mean is always the smallest value.
b. They are all equal.
c. The mean is always the largest value.
d. The mode is the largest value.
12. Data on 1,500 students' height were collected at a larger university in the East Coast. Which of the
following is the best chart for presenting the information?
a. a pie chart
b. a Pareto diagram
c. a side-by-side bar chart
d. a histogram
13. A random sample from an unknown population had a sample standard deviation of zero. Which of
the following is a reasonable conclusion?
a. The sample range must be zero.
b. An error was made in computing the sample standard deviation. It must always be greater
than zero.
c. The population standard deviation must be zero.
d. None of these.
false
false