Questions
Syllabus
Qns. By Syllabus

Semester

Subject

Year

Tribhuwan University

Institute of Science and Technology

2082

Bachelor Level / First Year / Second Semester / Science

Bachelors in Information Technology (STA154)

(Basic Statistics)

Full Marks: 60

Pass Marks: 24

Time: 3 Hours

Candidates are required to give their answers in their own words as for as practicable.

The figures in the margin indicate full marks.

Section A

Long Answers Questions

Attempt any TWO questions.
[2*10=20]
1.
The distribution of monthly incomes of 5,000 employees of a certain industrial unit was found to be normally distributed with mean of Rs. 2,000 and a standard deviation of Rs. 200. (i) Estimate the range of incomes of the middle 60% employees. (ii) Estimate the lowest income of richest 10% employees. (iii) Estimate the highest income of poorest 10% employees. [10+0+0+0]
2.
A software development team is tracking the build sizes (in MB) produced by two different automated build systems during nightly integrations over 10 days. Which build system is more consistent? Justify your answer.
Build System A88929485909589879186Build System B130135132140128133137131129138\begin{array}{|c|cccccccccc|}\hline \text{Build System A} & 88 & 92 & 94 & 85 & 90 & 95 & 89 & 87 & 91 & 86 \\ \hline \text{Build System B} & 130 & 135 & 132 & 140 & 128 & 133 & 137 & 131 & 129 & 138 \\ \hline \end{array}
[10]
3.
A web development team records the number of hours spent on debugging (X) and the number of resolved issues (Y) across 10 sprints.
X15202530354045505560Y36811121416192122\begin{array}{|c|cccccccccc|}\hline X & 15 & 20 & 25 & 30 & 35 & 40 & 45 & 50 & 55 & 60 \\ \hline Y & 3 & 6 & 8 & 11 & 12 & 14 & 16 & 19 & 21 & 22 \\ \hline \end{array}
a) Calculate the Pearson correlation coefficient to assess the relationship between debugging hours and issues resolved. b) Derive the regression equation of issues resolved on hours spent debugging. c) Predict the number of issues resolved for 38 hours of debugging. [10+0+0+0]
Section B

Short Answers Questions

Attempt any Eight questions.
[8*5=40]
4.
Differentiate Pareto chart and a bar diagram. [5]
5.
Fill the scale of measurement with the correct statistical test/measure.
VariableMeasurement ScaleBest Statistical MethodBlood groupStudents’ satisfaction (5-point Likert scale)Annual incomeAge group (18–25, 26–35, 36–45, 46+)The lifetime of an electronic device\begin{array}{|l|c|c|}\hline \text{Variable} & \text{Measurement Scale} & \text{Best Statistical Method} \\ \hline \text{Blood group} & & \\ \hline \text{Students’ satisfaction (5-point Likert scale)} & & \\ \hline \text{Annual income} & & \\ \hline \text{Age group (18–25, 26–35, 36–45, 46+)} & & \\ \hline \text{The lifetime of an electronic device} & & \\ \hline \end{array}
[5]
6.
A piece of equipment will function only when all the components A, B, and C are working. The probability of A failing during one year is 0.15, that of B failing is 0.05, and that of C failing is 0.10. What is the probability that the equipment will not fail before the end of one year? [5]
7.
Three persons A, B, and C are being considered for appointment as Vice-Chancellor of a university, and whose chances of being selected are in the proportion 4:2:3 respectively. The probability that A, if selected, will introduce democratization is 0.3, and the corresponding probabilities for B and C are 0.5 and 0.8. What is the probability that democratization would be introduced? [5]
8.
A tech team records the number of bug reports closed per hour. The probability distribution is given below. Find the expected number of bug reports closed per hour and its variance.
Y01234P(Y)0.100.180.320.300.10\begin{array}{|c|ccccc|}\hline Y & 0 & 1 & 2 & 3 & 4 \\ \hline P(Y) & 0.10 & 0.18 & 0.32 & 0.30 & 0.10 \\ \hline \end{array}
[5]
9.
A sample survey of 400 customers shows that 350 are satisfied with ABC company providing internet service. Estimate the proportion of satisfied customers in the market with 95% and 99% confidence interval. [5]
10.
It is observed that 80% of television viewers watch an entertainment channel. What is the probability that at least 80% of the viewers in a random sample of five watch an entertainment channel? [5]
11.
The first four moments about point 5 are 3, 10, 40, and 500. Compute the four central moments. [5]
12.
Write a short note on the following: (a) Cluster sampling (b) Primary data [5+0+0]