o E TX Reg No VIT Final Assessment Test May 2024 VIT 3 Vcllore Institute of Technology Slot E14TE1 Max Marks 100 KEEPING MOBILE PHONE ELECTRONIC DEVICES EVEN IN OFF POSITION IS TREATED AS EXAM MALPRACTICE DON T WRITE ANYTHING ON THE QUESTION PAPER Course Class NBR s 1752 1755 1757 1761 2338 Time Three Hours Statistics for Engineers MAT2001 General Instructions Statistical tables are permitted Answer any TEN Questions 10 X 10 100 Marks 1 The following data relates to the daily income of families in an urban area Find the 10 modal income of the families Income No of persons 5 0 100 100 200 200 300 300 400 400 500 500 600 600 700 7 12 18 16 10 5 2 The weekly sales of two products A and B were recorded as given below 10 Product A 59 75 27 63 27 28 56 Product B 150 200 125 310 330 250 225 3 Using coefficient of variation find out which of the two shows greater fluctuations in sales A mail order computer business has six telephone lines Let X denote the number of lines in use at a specified time Suppose the pmf of X is given in the accompanying table 10 0 1 2 3 4 5 6 pl 10 15 20 25 20 06 04 Calculate the probability of each of the following events i at most three lines are in use i1 fewer than three lines are in use iii at least three lines are in use iv between two and five lines inclusive are in use v between two and four lines inclusive are not in use A bank operates both a drive up facility and a walk up window On a randomly selected day let X be the proportion of time that the drive up facility is in use at least one customer is being served or waiting to be served and Y be the proportion of time that the walk up window is in use Then the set of possible values for X Y is the rectangle D x y 0 xs 1 0 S ys1 Suppose the joint pdf of X Y is given by 10 4 6 t9 0s xs 1 0sys1 0 otherwise i ii Verify whether f x y is probability density function Find P 0 SX 0sYs Find the marginal density functions fx x and f Page 1 of 3 Suppose on the basis of observation on hens in poultry the number of eggs laid by hens X1 depends on food X2 and types of hen X3 It is found that r12 0 8 r13 0 65 and r23 0 7 Find the partial correlations between three variables r12 3 r13 2 and r23 1 The following data gives the experience of machine operators and their performance ratings as given by the number of good parts turned out per 50 pieces Obtain the two regression equations and estimate the ratings Y corresponding to the experience x 15 10 10 6 Operations Experience X 8 11 Ratings Y 2 3 4 5 6 11 7 30 25 10 125 6 44 38 25 20 27 7 4 In a street of 200 families 40 families purchase the Hindu newspaper Among the families a sample of 10 families is selected find the probability that i Only one family purchase the news paper ii No family purchasing ii Not more than one family purchase it Students of a class were given an aptitude test Their marks were found to be normally distributed with mean 60 and standard deviation 5 What percentage of students scored 10 10 8 i iii more than 60 marks less than 56 marks between 45 and 65 marks 9 10 A civil service examination was given to 200 people On the basis of their total scores they were divided into the upper 30 and the remaining 70 On a certain question 40 of the upper group and 80 of the lower group answered correctly On the basis of this question is this question likely to be useful for discriminating the ability of the type being tested Use level of the significance 5 Southern Marketing Association the effect of shelf height on the supermarket sales of dog food is investigated The experimental data is given as follows 10 10 Knee Level Shelf Height Waist Level Eye Level 77 82 86 78 81 86 7 81 88 94 93 90 91 94 90 87 85 85 87 81 80 79 87 93 Using the completely randomized design CRD is there a significant difference in the average daily sales of this dog food based on shelf height Use a O 05 level of significance 11 A packet consists of 100 ball pens The distribution of the number of defective balI 10 pens in each packet is given below 0 61 1 14 2 10 3 7 4 5 5 3 f Examine whether Poisson distribution is appropriate for the above data at 5 level of significance 12 The time to failure in operating hours of a critical Solid state power unit has the 10 hazard rate function 2 t 0 003 0 5 for t 0 500 What is the reliability if the power unit must operate continuously for 50 hours ii Determine the design life if a reliability of 0 90 is desired ii Compute the MTTF SSS o E TXSS