Questions
Syllabus
Qns. By Syllabus

Semester

Subject

Year

Tribhuwan University

Institute of Science and Technology

2080

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.
Distinguish between descriptive and inferential statistics. The following table represents the mark obtained by a batch of 10 students in a certain class tests in Basic Statistics and Computer science. Indicate in which subject is the level of more consistency?
Marks in Basic Statistics53555232306047463558Marks in Computer science57452431258443803272\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}\hline \text{Marks in Basic Statistics} & 53 & 55 & 52 & 32 & 30 & 60 & 47 & 46 & 35 & 58 \\ \hline \text{Marks in Computer science} & 57 & 45 & 24 & 31 & 25 & 84 & 43 & 80 & 32 & 72 \\ \hline \end{array}
[10]
2.
Define regression. From the following table, compute the line of regression for estimating blood pressure: (i) Fit a regression equation that best describe the above data. (ii) Estimate the blood pressure when age is 50 yrs. (iii) Interpret the regression coefficient.
Blood pressure Y147125160118149128Age in years X564272366347\begin{array}{|c|c|c|c|c|c|c|c|}\hline \text{Blood pressure Y} & 147 & 125 & 160 & 118 & 149 & 128 \\ \hline \text{Age in years X} & 56 & 42 & 72 & 36 & 63 & 47 \\ \hline \end{array}
[10]
3.
Under which situation Normal distribution will be used. The annual salaries of employees in a large company are approximately normally distributed with a mean of $50,000 and a standard deviation of $20,000. (a) What is the probability of people earns less than $40,000? (b) What is the probability of people earns between $45,000 and $65,000? (c) What is the probability of people earns more than $70,000? [10]
Section B

Short Answers Questions

Attempt any Eight questions.
[8*5=40]
4.
Describe the role of Statistics in information technology. [5]
5.
The following table shows the mode of transport used by 400 students of a school. Represent the following information on the bar diagram and Pareto diagram.
Mode of transportBusBicycleOn footBy carNo. of students2001008020\begin{array}{|c|c|c|c|c|}\hline \text{Mode of transport} & \text{Bus} & \text{Bicycle} & \text{On foot} & \text{By car} \\ \hline \text{No. of students} & 200 & 100 & 80 & 20 \\ \hline \end{array}
[5]
6.
Write properties of correlation. A study is made relating aptitude scores to productivity in a factory after six months training of personnel. The following are the figures regarding six randomly selected workers: Find the coefficients of correlation between aptitude score and productivity index and comment on the value. Also find coefficient of variation for each variable
Aptitude Scores X91818202023Productivity Index Y123323422930\begin{array}{|c|c|c|c|c|c|c|c|}\hline \text{Aptitude Scores X} & 9 & 18 & 18 & 20 & 20 & 23 \\ \hline \text{Productivity Index Y} & 12 & 33 & 23 & 42 & 29 & 30 \\ \hline \end{array}
[5]
7.
Define random variable. A random variable X has following probability functions. Find, (i) The value of C. (ii) P(X < 3), P(X ≥\geq 1). (iii) Mean and variance.
X012345P(X)0.1C0.22C0.3C\begin{array}{|c|c|c|c|c|c|c|c|}\hline X & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline P(X) & 0.1 & C & 0.2 & 2C & 0.3 & C \\ \hline \end{array}
[5]
8.
Define binomial distribution. Fit a binomial distribution on the following data:
x01234f286246104\begin{array}{|c|c|c|c|c|c|}\hline x & 0 & 1 & 2 & 3 & 4 \\ \hline f & 28 & 62 & 46 & 10 & 4 \\ \hline \end{array}
[5]
9.
The probability that an integrated circuit chip will have defective etching is 0.12, the probability that it will have crack defect is 0.29, and the probability that it has both defects is 0.07. What is the probability that a newly manufactured chip will have either an etching or crack defect. [5]
10.
If the first four moments about mean are 0, 2.8, -2 and 24.5 respectively. Compute coefficient of skewness and kurtosis and comment upon result. [5]
11.
The fuel consumption of a new model of cars is being tested. In one trial, 50 cars chosen at random were driven under the identical conditions and the distances, x km, covered on 1 liter of petrol were recorded. The results gave the following totals: Σ x = 525, Σ x² = 5625. Calculate the 99% confidence interval for the mean petrol consumption, in km per liter. Interpret the result. [5]
12.
Write short note on the following: a) Use of Box and whisker plot. b) Parameter and Statistic. [5]