Maths Questionner

7/30/2019 Maths Questionner

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1. The mode of the numbers 7,7,7,9,10,11,11,11,12 is

a) 11 b) 12 c) 7 d) 7 and 11

2.

Average scores of three batsmen A, B, C are respectively 40, 45 and 55 and their standard deviations are respectively 9, 11, and 16. Which batsman is more consistent?a) A b) B c) C d) A and B

3. If the moment generating function of a random variable is 4(1 2 )t , then E(X) is

a) 8 b) 2 c) 16 d) 4

4. If p(B) =0.81 and ( ) 0.18, ( / ) p A B then p A B is

a) 1 b) 0.22 c) 4.5 d) 0

5. If X is a binomial variate with p=1/5 for the experiment of 50 trials, then the standard

deviation isa) 2 b) 8 c) 2 2 d) 10

6. The area under the normal curve is

a) 1 b) 0.5 c) 2 d) 1

7. Range of F-distribution is

a) (0, ) b) ( , ) c) (-1,1) d) (0,1)

8. A hypothesis is false, but accepted this is called

a) Type I error b) Type II error c) No error d) both a and b

9. Control chart for fraction defective is also called

a) p-chart b) x

-chart c) np-chart d) c-chart

10. The theoretical basis for c-chart is ------------ distributiona) Binomial b) Poisson c) Normal d) Exponential

...contd 2

Answer ALL Questions

Part B (10 2=20 Marks)

11. Write down the formula for median

12. What is the correction factor in the rank correlation.

13. If and B are independent events with p (A) =0.4 and p (B) =0. 5, then find ( ) p A B



14. Given that the probability density function of a random variable is f(x) = kx,

0< x < 1. Find the value of k.

15. If X is uniformly distributed over (0, 10), then find p(X<2)

16. If the probability that a target is destroyed on anyone shot is 0.5, what is the probability that it would be destroyed on 6

thattempt.

17. What are the uses of Student’s ‘t’ distribution.

18. What are the expected frequencies of 2 2 contingency table.

19. What do you mean by one-way classification in analysis of variance.

20. When the process is control and if n = 6 , x = 62.69 and R =19.67, find the tolerance

limits.

Part C (5 14= 70 Marks )

21. a (i) Find the mean and standard deviation for the following table giving the agedistribution of 542 members.

Age (in Years) : 20-30 30-40 40-50 50-60 60-70 70-80 80-90

No. of members : 3 61 132 153 140 51 2

(ii) Find the correlation coefficient from the following data

x : 77 54 27 52 14 35 90 25 56 60

y : 35 58 60 40 50 40 35 56 34 42

(Or)

...contd 3

(b) (i) Following are the marks obtained by the two students A and B are 10 sets of

ExaminationSets : 1 2 3 4 5 6 7 8 9 10

Marks obtained by A : 44 80 76 48 52 72 68 56 60 64

Marks obtained by B : 48 75 54 60 63 69 72 51 57 56If the consistency of performance in the criterion for awarding the prize, then

Who should get the prize?

(ii) The following table shows the ages (x) and blood pressure (y) of 8 persons



x : 52 63 45 36 72 65 47 25

y : 62 53 51 25 79 43 60 33

Obtain the regression equation y on x and find the expected blood pressure

of a person who is 49 years old.

22. (a) (i) In a bolt factory, machines A, B and C manufacture respectively 25%,35%and 40% total output. Also out of these output of A, B, and C. 5,4,2 percentrespectively are defective. A bolt is drawn at random from the total output

and it is found to be defective. What is the probability that it was

manufactured by the machine B?

(ii) Let X be the random variable law 1( ) , 1, 2,3,...r p X r q p r . Find the

Moment generating function and hence find its mean and variance assume

p+q=1..

(Or)(b) (i) A bag contains 5 red and 3 green balls and a second bag 4 red and 5 green

balls. One of the bags is selected at random and a draw of 2 balls is made

from it. What is the probability that one of them is red and the other is green.

(ii) A random variable X has the following probability function

X : 0 1 2 3 4 5 6 7

p(X) : 0 k 2k 2k 3k 2k 22

k 7 2k +k find (i) the value of k

(ii) ( 6) , ( 6) p X p X

(iii) If

1

( ) ,2 p X c

find the minimum value of c.

23. (a)(i) A machine manufacturing screws is known to produce 5% defective. In arandom sample of 15 screws, what is the probability that there are

(i) exactly 3defectives.

(ii) not more than 3 defectives

...contd 4(ii) The length of time a person speaks over phone follows exponential

distribution with mean 1/6. What is the probability that the person

will talk for (i) more than 8 minutes (ii) between 4 and 8 minutes.

(Or)

(b) (i) If X is a Poisson variate such that p(X=2)= 9p(X=4)+90p(X=6), find the

variance.

(ii) In a normal distribution 31% of the items are under 45 and 8% are over 64.

Find the mean and variance of the distribution.



24.(a)(i) The average hourly wage of a sample of 150 workers in a plant A was Rs.2.56

with standard deviation of Rs.1.08. The average wage of a sample of 200

workers in plant B was Rs.2.87 with a standard deviation of Rs.1.28. Can an

applicant safely assume that the hourly wages paid by plant B are higher thanthose paid by the plant A.

(ii) A sample analysis of examination results of 500 students was made. It wasfound that 200 students have failed, 170 have secured a third class, 90 have

secured a second class and the rest, a first class. So these figures support the

general belief that the above categories are in the ratio 4:3:2:1

(Or)

(b)(i) The average breaking strength of steel rods is specified to be 18.5 thousand

pounds. To test this sample of 14 rods was tested. The mean and standardobtain were 17.85 and 1.955 respectively. Is the result of the experiment

significant with 95% confidence limit..

(ii) In one sample of 8 observations the sum of the squares of deviations of the

value from the sample mean was 84.4 and in the other sample of 10

observations it was 102.6. Test whether this difference is significant at 5% level,

given that at 5 percent point of F for 1 27 9n and n d.f is 3.29.

25. (a) Perform two-way ANOVA for the given below.

Treatment

Plots of land A B C D

I 38 40 41 39

II 45 42 49 36III 40 38 42 42.

(Or)(b) 10 samples each of size 50 were inspected and the number of defectives in the

inspection were 2,1,1,2,3,5,5,1,2,3. Draw the p-chart for defectives.

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