Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU) B-Tech 3rd Semester (Third Semester) 2015-2016 NBT 301 Elementary Mathematics Iii Question Paper
(Following Paper ID and Roll No. to be filied in your
Answer Book)
Roll No.
B. Tech.
(SEM. HDTHEORY EXAMINATION, 2015-16
ELEMENTARY MATI-IEMATICS?III
[Time:3 hours] 1 [Total Marks:100]
Section-A
Q.l Attempt all parts. All parts can'y equal marks. Write answer
. of each question in short. ' (2x 10:20)
(a) Draw bar diagram to represent the following data:
Years 1959 1960 1961 1962 1963
WheatinQuantity 200' 350 450 550 600
(b) De?ne Binomialdistribution.
(c) Find out the arithmetic mean of the following data:
25, 30, 21, 55, 47, 10, 15, 17, 45, 35
((1) De?ne Statistical quality control.
(C) De?ne skewhess and Kurtosis. -
(f) I What" IS the probability that a leap year selected at
random will have 53 Sunday?
(1) NBT?1301
(g) Explain parametric & non-parameti'ic test.
(h) In a binomial distribution, the mean and SD. are 12
and 2 respectively, ?nd n and p.
(i) What do you mean by internal and extemai data?
0) Write down the Empirical relation and ?nd out the
mean, if mode=64.2 and median= 66.33.
Section?B ? \
Attempt any ?ve questions from this section. ( lOXS=50)
' Q.2 In a partially destroyed laboratory record of an analysis
Q3.
of a con'elation data, the follOwing results only are legible:
Variancqof x=9
Regression equation: 8x~10y+66=0, 40x-1 8y=2 14
To ?nd out
(i) the mean values of x, and y
(ii) the standard deviations of y.
(i) De?ne Sign test.?
(ii) Find the regression equation?_and coef?cient of
. correlation from the given data:
zx=60,>:x2 =4160,>:y=40,z_y2 =1720,zxy=1150,N=1o
(2) ' - NBT-30l
Q4. Obtain regre?sion plane by using multiple linear
regression of the following data: ' '
.x _ 1 ' 2. 3 4
12 . 18 24 30
z' 0 ? 1 2 3
Q5. The height of 6 randomly chosen sailors 'in inches is
63,65,68,69,71 and 72. Those of 9-r_andomly chosen?
soldiers are 61,62,65,66,?69,70,7 1,72,73. Test whether the
sailors are on the average taler than soldiers. (Given
?13. 0.05 =1-77)
Q6. Draw the Ogives and hence estimate the median of the
following data:
Class 0-9 10-19 20-29 30-39 40-49 50-60
Frequency 8 32 142 216 240 , 143
Q7. The folloWing table gives the classi?cation of 100 workers
according to sex and nature of work. Test whether nature
of work is independent of the sex of worker.
Give that Xzo?os (l) = 3.841
Skilled Unskilled Total
Male 40 20 60 '
Female 10 30 40
' Total 50 so '100
(3) P.T.O.
Q8. What'is Latin square Design? Under what conditions can
this Design be used? Discuss brie?y the advantages and
disadvantages of Latin square Design.
Q9.
State
What do you understand by two way analysis of variants?
by suitable example the methodology carrying out
analysis of vanants
Section-C
V Note: Attempt any two quiestions from this section.(15 ><2=30)
Q10. (i)
A company wants to test whether its three salesman
AB and C have the same selling ability. Their records
I of sales (in Rs. ?000) during various weeks of the
last month are given in the following'table?
\
Sa lesman
1"Week
2"? week
3rd Week
4'? Week
A
16
21
18
25
B
22
20
15
26'
C
25
24
16
20
(ii) 1
Prepare an analysis Of variance table and test the
hypothesis that the mean sales per-week of all
salesmen are equal.(F (2,9)=4.25)
0.05
Fit a Poisson distribution to the following set of
observations, and calculate the theoretical
frequencies.
(4) NBT?301
Deaths
0
1
? 2
. 3
122
60
15
2
1
Frequency
Q11. (i) The lifetme of electric bulbs for a random sample
of 10 from a lagge consignment gave the following
data:
Item
1 2 3-4 5 6 7 8 9 10
Life (hr)
4.2 4.6 3.9 4.1 5.2 3.8 3.9 4.3 4.4 5.6
(ii)
Can we accept the hypothesis that the average
lifetime of bulb is 4 hours? (At 5% level of
signi?cance value of t-statistic for_9 degree of
freedom is 2.26)
Two line of regression equations are given by x+2y-
5=0 & 2x+3y-8=0 and variance of x=1 2. Calculate
(i) the mean of x and y (ii) varianee of y (iii) the
correlation coef?cient.
De?ne rank correlation coef?cients. Obtain the rank
' cerrelation coef?cient for the following data:
x68647550648075405564?
y.62585845816,068485070
(5) NBT?301
(ii) Th? data of defective of 10 sample of size 50 each
7 are giycn below: ?
sambleho. 1 3 4- 5 6?7? 8 9 1o
No.0fdefectives 3 3 4 4 4 2 3 1
Construct p-chartl'and give your comment;
__X._
NBT-301/l400
(6)
This post was last modified on 29 January 2020