12223

22397
3 Hours / 70 Marks Seat No.

Instructions : (1) All Questions are compulsory.

(2) Illustrate your answers with neat sketches wherever necessary.
(3) Figures to the right indicate full marks.
(4) Use of Non-programmable Electronic Pocket Calculator is
permissible.

Marks
1. Attempt any FIVE of the following : 10
(a) Calculate harmonic mean of 4, 6, 8, 13, 14, 19.
(b) Find decile D5 for the following data :
21, 15, 40, 30, 26, 45, 50, 54, 60, 65, 70.
(c) Calculate mode using histogram.

C.I. 10-20 20-30 30-40 40-50

fi 2 5 9 6

(d) Find covariance of following data :

X 1 2 3 4 5

Y 2 3 4 6 10

(e) An unbiased coin is tossed 3 times. What is the probability of getting two
heads ?
(f) Find the probability of getting four heads in six tosses of a fair coin.
(g) A random sample of 20 items gives the mean 5.4, standard deviation 10.25
and population mean 2.4. Find the value of standard normal variate.

[1 of 4] P.T.O.
22397 [2 of 4]
2. Attempt any THREE of the following : 12
(a) The average marks of 50 students in class is 5. The pass result of 40 students
who took up a class test is given below. Calculate mean marks of 10 students
who failed.
Marks 4 5 6 7 8 9
No. of students 8 10 9 6 4 3
(b) Calculate median for following distribution :
C.I. 0-8 8-16 16-24 24-32 32-40 40-48
Freq. 8 10 16 24 15 7
(c) The following data gives the marks obtained by number of students. Calculate
median using ogive curve.
C.I. 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100
Freq. 5 3 4 3 3 4 7 9 7 8
(d) Calculate Spearman’s ranks correlation coefficient for following data :
X 35 54 80 95 73 76 35 91 83 81
Y 40 60 75 90 70 75 38 95 75 71

3. Attempt any THREE of the following : 12

(a) Calculate the measure of Kurtosis based on the moment for following data :
X 2 3 4 5 6
f 1 3 7 3 1
(b) Calculate Bouley’s coefficient of skewness of the following data :
C.I. 0-10 10-20 20-30 30-40 40-50 50-60
Freq. 3 8 2 10 4 13
(c) Fit a second degree parabola Y = ax2 + bx + c in least square for following
data :
X 1 2 3 4 5
Y 10 12 13 16 19
22397 [3 of 4]
(d) Calculate correlation coefficient for the following data :
X 9 8 7 6 5 4 3 2 1
Y 15 16 14 13 11 12 10 8 9

4. Attempt any THREE of the following : 12

(a) Calculate correlation coefficient of given data.
X 41 42 43 44 45
Y 3.2 3.3 3.4 3.5 3.6
(b) For 10 observations on price (x) and supply (y) the following data was
obtained :
x = 130, y = 220, x2 = 2288, y2 = 5506, xy = 3467.
Obtain the line of reflection of Y on X and estimate the supply when the price
is 16 units.
(c) A five digit number is formed by using the digits 0,1,2,3,4 & 5 without
repetition. Find the probability that the number is divisible by 6.
(d) A problem of statistics is given to three students A, B & C whose chances of
1, 3 1
solving it are & respectively. What is the probability that the problem
2 4 4
will be solved ?
(e) Three urn contains 6 red, 4 black; 4 red, 6 black; 5 red, 5 black balls
respectively. One of the urn is selected at random & a ball is drawn from it. If
the ball drawn is red, what is the probability that it is drawn from first urn ?

5. Attempt any TWO of the following : 12

(a) Attempt the following :
(i) If 20% of the bolts produce by a machine are defective. Find the
probability that out of 4 bolts drawn atmost two are defective.
(ii) The probability that a man aged 60 years will live upto 70 is 0.65. What
is the probability that out of ten men which are now 60 years, at least 7
would live upto 70 years ?
P.T.O.
22397 [4 of 4]
(b) Number of road accidents follows a Poisson distribution with mean 5. Find
the probability that in a certain month number of accidents on the highway
will be more than 3.
(c) In a certain examination 500 students appeared average score is 68 with
standard deviation 8. Find the number of students scoring : (a) less than 50
(b) more than 60. (Given A(2.25) = 0.4878, A (1) = 0.3413)

6. Attempt any TWO of the following : 12

(a) Attempt the following :
(i) A manufacturer intends that his electric bulbs have a life of 1000 hours.
He tests a sample of 20 bulbs, drawn at random from a batch &
discovers that the mean life of sample bulbs is 990 hours with standard
deviation 22 hours. Find ‘t’ using t-distribution & signify that the batch
is not upto the standard.
(Given : The table value of t at 1% level is significance with 19 degrees
of freedom is 2.539.)
(ii) In a sample of 800 men from a certain city 600 are found smokers. In
another sample of 1000 men from another city 500 are smokers. Find
standard normal variate ‘Z’ using sampling distribution of proportions.
(b) A cubical die was thrown 9000 times and 1 or 6 was obtained 3120 times. Can
the deviation from expected value lie due to fluctuations of sampling ?
(c) A survey of 800 families with four children each revealed the following
distribution :
No. of boys 0 1 2 3 4
No. of girls 4 3 2 1 0
No. of families 32 178 290 236 64
Is this result consistent with the hypothesis that male and female births are
equally probable ?
_______________