Probability And Statistics | Week 8

Probability And Statistics Week 8 Answers

Link : Probability And Statistics (nptel.ac.in)

Q1. The distance, in meters for eight throws of a shotputter are shown below
15.92,16.27,15.41,18.48,17.28,14.98, 15.85
Calculate sample mean and sample standard deviation.
(A) 16.31,1.11
(B) 16.31,1.19
(C) 16.31,1.43
(D) 16.31,1.22

Q2. Consider the following frequency table.

Calculate the median.
(A) 37.95
(8) 51.21
(C) 31.56
(D) 38.13

Q3. Suppose X,Y, Z are three independent chi-square random variables with 1,4,9 degrees of freedom respectively, then distribution of X + Y + Z is _________.
(A) X²(15)
(B) N(0,14)
(C) X²(14)
(D) X²(12)

Q4. What is the median of the following dataset
31,6,12,27,17,15,21,13,2
(A) 15
(B) 17
(C) 16
(D) 2

Q5. Calculate the mode of question 2.
(A) 33.19
(B) 36.81
(C) 36.19
(D) 33.81

Q6. Consider the following data
A : 200 300 500 700 900
B : 100 150 270 800 500
Suppose CVA and CVB denote the coefficient of variations of set A and set B respectively. Select the correct statement(s).
(A) CVA > CVB
(B) CVB > CVA
(C) Mean of set A > Mean of set B
(D) Mean of set A< Mean of set B

Q7. Suppose the observations are arranged in ascending order and given as
15 x 21 x+10 30 39
Find x if median of the set is 24.
(A) 27
(B) 22
(C) 17
(D) 20

Q8. Consider the following grouped data

Find mode.
(A) 54.32
(B) 53.68
(C) 49.32
(D) 48.68

Q9. Here are measurements of photoresist thickness for eight wafers baked at two different temperatures. Find the standard deviation on the difference in thickness.

(A) 2.2197
(B) 3.075
(C) 3.56
(D) 5.21

Q10. The runs scored in a cricket match by 11 players are as follows
5,15,115,17,71,29,62,2,15,15,1
The (mean, median, mode) is _______.
(A) (31.5,15,15)
(B) (31.5,17,15)
(C) (49.5,29,15)
(D) (35.5,29,15)