INSTITUTE OF APPLIED STATISTICS, SRI LANKA
NATIONAL STATISTICS OLYMPIAD
STRUCTURE OF THE PAPER - 2012 ONWARDS
1. This paper consists of two parts, Part A and Part B, where Part A includes 20 multiple choice
questions and Part B includes 30 multiple choice questions.
2. When allocating marks, any question in Part B will be given double weightage of any question in
Part A. Total marks for the paper is 120.
3. Time allocation for answering the whole paper is TWO HOURS.
4. For any incorrect answer minus marks, as decided by the examination panel, will be given.
5. Candidates are requested to underline the most appropriate answer for each question.
6. Use of calculator is NOT allowed.
Sample questions for PART A
1. Which of the following is a discrete quantitative random variable?
a)
b)
c)
d)
e)
The volume of water released daily from a dam.
The distance you walk in a day.
The number of employees of an insurance company absent in a day.
The weight of school children sampled in a nationwide study.
None of the above.
2. Which of the following is not suitable to summarize data collected on a continuous random variable?
a) Histogram.
b) Bar chart.
c) Frequency polygon.
d) Stem and Leaf plot.
e) Box plot.
3. Given below are marks(out of 100) obtained for a mathematics test by fifteen students:
45, 67, 59, 40, 75, 42, 60, 55, 78, 40, 52, 73, 65, 40, 65
The median mark is
a) 40
b) 55
c) 57
d) 59
e) None of the above
4. In general, which of the following descriptive summary measures cannot be approximated from a
Box plot?
a) The variance.
b) The range.
c) The interquartile range.
d) The median.
e) The maximum.
5. A survey was conducted to determine how people rated the quality of programms available on television.
Respondents were asked to rate the overall quality from 0 (no quality at all) to 100 (extremely good
quality). The stem-and-leaf plot of the collected data is shown below.
Stem
3
4
5
6
7
8
9
Leaves
24
03478999
0112345
12566
01
2
What percentage of the respondents rated overall television quality with a rating of 50 or below?
a) 11
b) 40
c) 42
d) 44
e) 56
6.
How many ways can six persons be assigned offices if there are 10 rooms available?
a)
10
C6
b)
10
P6
c) 6!
d) 10!
e) None of the above
7. If two events are mutually exclusive and collectively exhaustive, what is the probability that one or the
other occurs?
a) 0.
b) 0.25.
c) 0.50.
d) 1.00
e) Cannot be determined from the information given.
8.
A fair coin is tossed three times. If the coin lands with the head up on the first two tosses, what is the
probability that the coin will land with the head up on the third toss?
a) 0
b) 1/8
c) ¼
d) ½
e) None of the above
9. A recent survey of banks revealed the following distribution for the interest rate being charged on a
housing loan scheme (based on a 30-year mortgage with a 10% down payment).
Interest Rate
Probability
7.0%
0.12
7.5%
0.23
8.0%
0.24
8.5%
0.35
> 8.5%
0.06
If a bank is selected at random from this distribution, what is the chance that the interest rate charged on
a housing loan will exceed 8.0%?
a) 0.06
b) 0.41
c) 0.59
d) 0.80
e) 1.00
10. Suppose A and B are independent events such that P(A) = 0.4 and P(B) = 0.5. Then P(A or B) is
a) 0.2
b) 0.45
c) 0.6
d) 0.7
e) 0.9
Sample questions for PART B
1. Given below is the stem-and-leaf plot representing the amount of detergent used in liters (with leaves in
10ths of liters) in a month by 25 service stations.
9 | 147
10 | 02238
11 | 135566777
12 | 223489
13 | 02
What is the percentage of service stations that use “12.0 or more but less than 13.0 liters” of detergent per
month?
a) 14% b) 16%
c) 22%
d) 24%
e) 25%
2. Consider the following frequency distribution.
x 0 1 2 3 4 5 6 7 8
f 1 2 3 4 7 11 17 11 4
Which of the following is true?
a) The distribution is symmetric
b) The distribution is positively skewed
c) The distribution is negatively skewed
d) Mean is grater than median
e) Median is greater than mode
3. The following summary statistics are given for a data set:
Mean = 9.63,
Variance = 23.98,
Median = 9.50,
The coefficient of variation of the data set is
a) 50.88
b) 51.58
c) 196.5
d) 249.0
Range = 14
e) None of the above
4. What are the mean and standard deviation of the data set
{11 15 23 29 19 22 21 20 15 25} which represent the amount of grams of carbohydrates in a
serving of breakfast cereal in a sample of 11 different servings?
a) 18.2, 6.15
b) 20.0, 5.29
c) 20.0, -6.15
d) 21.2, 6.15
e) 21.2, -7.50
5. What are the range and interquartile range of the data set
{11 15 23 29 19 22 21 20 15 25 17} which represent the amount of grams of carbohydrates in a
serving of breakfast cereal in a sample of 11 different servings?
a) 8, 10
b) 8, 12
c) 15, 8
d) 18, 8
e) 18, 10
6. Vehicle license plates consist of letters and numbers. There are 26 letters and the letters may be repeated.
There are 10 digits and the digits may be repeated. How many possible license plates can be issued with
two letters followed by three numbers provided that all three digits cannot be zero.
a) 26x25x10x9x8
b) 26x25(103)
c) 262(103-1) d) 262(103)
e) None of the above
7. Given P(A) = 0.35, P(B) = 0.25, and P(AB) = 0.18, which of the following is correct?
a) P(AB) = 0.42
b) P(AB) = P(A) + P(B)
c) P(A|B) = 0.72
d) Both (a) and (c)
e) Both (a) and (b)
8. A company has 2 machines that produce fire crackers. An older machine produces 23% defective fire
crackers, while the new machine produces only 8% defective fire crackers. In addition, the new machine
produces 3 times as many fire crackers as the older machine does. Given that a fire cracker was produced
by the new machine, what is the probability it is not defective?
a) 0.06
b) 0.50
c) 0.86
d) 0.92
e) 0.94
9. Suppose the events B1, and B2, are mutually exclusive and collectively exhaustive events
with P(B1) = 0.4, P(B2) = 0.6. Another event A has the conditional probabilities P(A|B1) = 0.4, and
P(A|B2) = 0.25. Then P(A) is
a) 0.15
b) 0.16
c) 0.31
d) 0.65
e) None of the above
10. Bowl A contains 2 red chips; bowl B contains two white chips; and bowl C contains 1 red chip
and 1 white chip. A bowl is selected at random, and one chip is taken at random from that
bowl. If the selected chip is white, what is the probability that the other chip in the bowl is red?
a) 1/3
b) ½
c) 3/5
d) 5/6
e) None of the above