Questions
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Qns. By Syllabus

Semester

Subject

Year

Bachelors Level/First Year/Second Semester/Science bit/second semester/basic statistics/syllabus wise questions

Bachelors In Information Technology

Institute of Science and Technology, TU

Basic Statistics (STA154)

Year Asked: 2078, syllabus wise question

Correlation and Linear Regression
1.
The following data gives the experience of Computer Operators in years and their performance as given bt the number of good parts turned out per 100 pieces. i) Fit the regression equation of performance rating in experience. ii) Estimate the probable performance of an operator had 8 years of experience and interpret regression coefficient.

$\begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline \text{Experience (X)} & 16 & 12 & 18 & 4 & 3 & 10 & 5 & 12 \\ \hline \text{Performance (Y)} & 87 & 88 & 89 & 68 & 78 & 80 & 75 & 83 \\ \hline \end{array}$
[10]
2.
Define correlation coefficient? Calculate the co-efficient of correlation for the following ages(in years) of husbands and wives and interpret it.

$\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|}\hline \text{Husband's age X:} & 23 & 27 & 28 & 28 & 29 & 30 & 31 & 33 & 35 & 36 \\ \hline \text{Wife's age Y:} & 18 & 20 & 27 & 21 & 29 & 27 & 27 & 29 & 28 & 29 \\ \hline \end{array}$
[5]
Descriptive Statistics
1.
What are different methods of measuring dispersion? Following are the marks of Basic Statistics obtained by two students A and B in 10 tests of 100 marks each. i) Who is better? ii) If the consistency of performance is the criteria for awarding a prize, who should get the prize?

$\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|}\hline \text{Test} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline \text{Mark of A} & 44 & 80 & 76 & 48 & 52 & 72 & 68 & 56 & 60 & 54 \\ \hline \text{Mark of B} & 48 & 75 & 54 & 60 & 63 & 69 & 72 & 51 & 57 & 66 \\ \hline \end{array}$
[10]
2.
The standard deviation of a symmetric distribution is 7. Compute the possible value of fourth central moment for the distribution to be (i) mesokurtic (ii) platykurtic, and (iii) leptokurtic. [5]
3.
Write short notes on the following: a.) Choice of appropriate measure of central tendency b.)Parameter and statistic [5]
Diagrammatical and Graphical Presentation of Data
1.
The following table shows the numbers of hours spent by a child on different events on a working day. Represent the adjoining information on a pie chart.

$\begin{array}{|l|c|}\hline \text{Activity} & \text{No. of hours} \\ \hline \text{School} & 6 \\ \text{Sleep} & 8 \\ \text{Playing} & 2 \\ \text{Study} & 4 \\ \text{T.V.} & 1 \\ \text{Others} & 3 \\ \hline \end{array}$
[5]
Introduction
1.
What is measurement of scale? Describe different types of measurement scale. [5]
Introduction to Probability
1.
Suppose that after 10 years of service, 40% of computers have problems with motherboards (MB), 30% have problems with hard drives (HD), and l5% have problems with both MB and HD. What is the probability that a 10-year old computer still has fully functioning MB and HD? [5]
Probability Distributions
1.
During one stage in the manufacture of integrated circuit chips, a coating must be applied. If 70% of chips received a thick enough Coating. find the probability that among 15 chips (1) at least 12 will have thick enough coatings, and (2) exactly 10 will have thick enough coatings. [5]
2.
Define standard normal distribution. For a certain type of computers, the length of time between charges of the battery is normally distribbuted with a mean of 50 hours and a standard deviation of 15 hours. He owns one of these computers and wants to know the probability that the length of time will be (i) between 50 and 70 hours, (ii) more than 60 hours, and (iii) less than 45 hours? [10]
Random Variables and Mathematical Expectation
1.
Suppose a continuous random variable X has the density function. Find; (i) value of k, (ii) P (0 < x < 0.5), and, (iii) E(X) and (iv) E(2X + 4)

$f(x) = \begin{cases} k(1-x)^2; & \text{for } 0 < x < 1 \\ 0; & \text{elsewhere} \end{cases}$
[5]
Sampling and Sampling Distribution
1.
Describe sampling error and non-sampling error. [5]