Questions
Syllabus
Qns. By Syllabus

Semester

Subject

Year

Credit:Nikesh DhimalNikesh Dhimal

Tribhuwan University

Institute of Science and Technology

2080.1

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.
Explain which measure of central tendency is suitable under which situation? Two computer manufacturers A and B compete in their rivalry, each claim that their computer is consistent. For this, it was decided to start execution of the same program simultaneously on 50 computer of each company and recorded the time as given below. What is the average life of each of these computers? Which company’s computer is more consistent?
Time (in second)0−22−44−66−88−1010−12Computer A51613754Computer B27121991\begin{array}{|c|cccccc|}\hline \text{Time (in second)} & 0-2 & 2-4 & 4-6 & 6-8 & 8-10 & 10-12 \\ \hline \text{Computer A} & 5 & 16 & 13 & 7 & 5 & 4 \\ \hline \text{Computer B} & 2 & 7 & 12 & 19 & 9 & 1 \\ \hline \end{array}
[10]
2.
What are the assumptions of applying simple linear regression model? A computer manager is interested to know the efficiency of his new computer program which depends on the size of incoming data. Efficiency will be measured by the number of processed requests per hour. Applying the program to data sets of different sizes, the following data were gathered. (a) Identify which one response variable and fit a simple regression line assuming that the relationship is linear. (b) Interpret the regression coefficient with reference to your problem. (c) Based on the fitted model predict the efficiency of new computer for data size 16 (gigabytes).
Data size (gigabytes)89107121518Processed requests41544551171614\begin{array}{|c|ccccccc|}\hline \text{Data size (gigabytes)} & 8 & 9 & 10 & 7 & 12 & 15 & 18 \\ \hline \text{Processed requests} & 41 & 54 & 45 & 51 & 17 & 16 & 14 \\ \hline \end{array}
[10]
3.
Discuss the measure properties of normal distribution. The burning time of an experimental rocket is a random variable having the normal distribution with mean 4.76 seconds and standard deviation 0.04 second respectively. What is probability that this kind of rocket will burn (i) Less than 4.68 seconds (ii) More than 4.80 seconds (iii) Anywhere from 4.70 to 4.82 seconds?
μ=4.76,σ=0.04\mu = 4.76, \quad \sigma = 0.04
P(X<4.68),  P(X>4.80),  P(4.70<X<4.82)P(X < 4.68), \; P(X > 4.80), \; P(4.70 < X < 4.82)
[10]
Section B

Short Answers Questions

Attempt any Eight questions.
[8*5=40]
4.
Highlight the difference between descriptive and inferential statistics. Describe the role of Statistics in information technology. [5]
5.
Construct bar diagram and Pareto diagram of the following information.
BrandDellAcerLenovoHPTotalNo. of Sales501004060250\begin{array}{|c|cccc|c|}\hline \text{Brand} & \text{Dell} & \text{Acer} & \text{Lenovo} & \text{HP} & \text{Total} \\ \hline \text{No. of Sales} & 50 & 100 & 40 & 60 & 250 \\ \hline \end{array}
[5]
6.
From the following data on marks of 10 students in the two subjects, calculate the Karl Pearson’s coefficient of correlation r and interpret the result.
Maths55704030908060809080Basic Statistics65403050607050506070\begin{array}{|c|cccccccccc|}\hline \text{Maths} & 55 & 70 & 40 & 30 & 90 & 80 & 60 & 80 & 90 & 80 \\ \hline \text{Basic Statistics} & 65 & 40 & 30 & 50 & 60 & 70 & 50 & 50 & 60 & 70 \\ \hline \end{array}
[5]
7.
A jewelry dealer is interested in purchasing gold necklace for which probabilities are 0.18, 0.22, 0.33 and 0.27 respectively that it will be sold for a profit of Rs. 5000, Rs. 8000, 6000 and sell for a loss of Rs. 3000. Find expected profit and variance of profit. [5]
8.
Fit a Poisson distribution to the following data.
Defects (X = x)012345Number of pages142156692751\begin{array}{|c|cccccc|}\hline \text{Defects (X = x)} & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline \text{Number of pages} & 142 & 156 & 69 & 27 & 5 & 1 \\ \hline \end{array}
[5]
9.
The odds in against of A solving a problem as 8 to 6 and the odds in favor of B solving the same problem are 14 to 10. What is the probability that (a) both A and B will solve it? (b) A solve it but B fails to solve it? [5]
10.
Drive D of a computer having 25 folders contain the following number of files. (a) List the five number summaries (b) Construct a box-plot for the data (c) Are the data skewed?
4,0,5,2,3,1,4,3,2,3,4,3,1,6,3,2,3,4,2,1,0,3,2,5,44, 0, 5, 2, 3, 1, 4, 3, 2, 3,4,3, 1, 6, 3, 2, 3, 4, 2, 1, 0, 3, 2, 5, 4
[5]
11.
Define interval estimation. In an examination, the random sample of 10 students selected from examination and their marks obtained in an examination was 45, 55, 20, 54, 40, 55, 51, 35, 43 and 46. Find 99% confidence interval for population mean. Assuming that the population from which samples are drawn is normally distributed. [5]
12.
Write short notes on any two: (a) Sampling and non-sampling error (b) Parameter and statistic. [5]