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#### Probability Distributions Model Question Paper

12th Standard EM

Reg.No. :
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Time : 01:30:00 Hrs
Total Marks : 50
6 x 1 = 6
1. Normal distribution was invented by

(a)

Laplace

(b)

De-Moivre

(c)

Gauss

(d)

all the above

2. If Z is a standard normal variate, the proportion of items lying between Z = –0.5 and Z = –3.0 is

(a)

0.4987

(b)

0.1915

(c)

0.3072

(d)

0.3098

3.  In turning out certain toys in a manufacturing company, the average number of defectives is 1%. The probability that the sample of 100 toys there will be 3 defectives is

(a)

0.0613

(b)

0.613

(c)

0.00613

(d)

0.3913

4. A manufacturer produces switches and experiences that 2 per cent switches are defective. The probability that in a box of 50 switches, there are atmost two defective is :

(a)

2.5 e-1

(b)

e-1

(c)

2e-1

(d)

none of the above

5. The average percentage of failure in a certain examination is 40. The probability that out of a group of 6 candidates atleast 4 passed in the examination are:

(a)

0.5443

(b)

0.4543

(c)

0.5543

(d)

0.4573

6. The random variable X is normally distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is between 72 and 84?

(a)

0.683

(b)

0.954

(c)

0.271

(d)

0.340

7. 7 x 2 = 14
8. Define Binomial distribution.

9. Define Bernoulli trials.

10. Write down the conditions for which the binomial distribution can be used.

11. Mention the properties of binomial distribution.

12. If the probability of success is 0.09, how many trials are needed to have a probability of atleast one success as 1/3 or more ?

13. The mean of a binomial distribution is 5 and standard deviation is 2. Determine the distribution.

14. Write any 2 examples for Poisson distribution.

15. 5 x 3 = 15
16. A fair coin is tossed 6 times. Find the probability that exactly 2 heads occurs.

17. In tossing of a five fair coin, find the chance of getting exactly 3 heads.

18. Suppose A and B are two equally strong table tennis players. Which of the following two events is more probable:
(a) A beats B exactly in 3 games out of 4 or
(b) A beats B exactly in 5 games out of 8 ?

19. Assume the mean height of children to be 69.25 cm with a variance of 10.8 cm. How many children in a school of 1,200 would you expect to be over 74 cm tall?

20. Weights of fish caught by a traveler are approximately normally distributed with a mean weight of 2.25 kg and a standard deviation of 0.25 kg. What percentage of fish weigh less than 2 kg?

21. 3 x 5 = 15
22. In a book of 520 pages, 390 typo-graphical errors occur. Assuming Poisson law for the number of errors per page, find the probability that a random sample of 5 pages will contain no error.

23. If the probability that an individual suffers a bad reaction from injection of a given serum is 0.001, determines the probability that out of 2,000 individuals (a) exactly 3, and (b) more than 2 individuals will suffer a bad reaction.

24. When counting red blood cells, a square grid is used, over which a drop of blood is evenly distributed. Under the microscope an average of 8 erythrocytes are observed per single square. What is the probability that exactly 5 erythrocytes are found in one square?