Download WBUHS 2nd Year 2022 May Microbiology Paper II Question Paper

1. Define probability.
2. State Baye's theorem.
3. Define random variable.
4. Write the formula for the mean of the Poisson distribution.
5. Define null hypothesis.

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6. What is critical region?
7. Write the formula for Spearman's rank correlation coefficient.
8. Define regression lines.
9. Define queuing theory.
10. What are the characteristics of a queuing model?

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PART-B

(Answer any three questions. Each question carries 20 marks)

1. 2. a) In a bolt factory machines A, B, and C manufacture respectively 25%, 35% and 40% of the total. Of their output 5, 4, and 2 percent are defective bolts. A bolt is chosen at random from the production and is found to be defective. What is the probability that it was manufactured by machine A.

   b) 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	K2	2K2	7K2+K

   Find i) K ii) Evaluate P(X<6), P(X≥6) and P(0<X<5)

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2. 3. a) Out of 800 families with 5 children each, how many would you expect to have (i) 3 boys (ii) at least one boy (iii) no girl (iv) all girls. Assume equal probabilities for boys and girls.

   b) Fit a Poisson distribution to the following data

   x	0	1	2	3	4
   f	200	90	30	5	2

3. 4. a) The means of two large samples of sizes 1000 and 2000 members are 67.5 inches and 68.0 inches respectively. Can the samples be regarded as drawn from the same population of standard deviation 2.5 inches?

   b) A random sample of 500 apples was taken from a large consignment and 65 were found to be bad. Obtain 95% confidence limits for the percentage of bad apples in the consignment.

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4. 5. a) Two random samples are drawn from two normal populations are:

   Sample 1: 20, 16, 26, 27, 23, 22, 18, 24, 25, 19

   Sample 2: 27, 33, 42, 35, 32, 34, 38, 28, 41, 43, 30, 37

   Test whether the samples are drawn from the same population. [10M]

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   b) The following table gives the number of aircraft accidents that occurred during the various days of a week. Test whether the accidents are uniformly distributed over the week.

   Days	Sun	Mon	Tue	Wed	Thu	Fri	Sat
   No. of accidents	14	16	8	12	11	9	14

5. 6. a) Calculate Karl Pearson’s correlation coefficient from the following data:

   x	10	12	13	16	17	20	23	25
   y	12	15	15	18	19	22	24	25

   b) If two regression equations are x + 3y = 7 and 2x + 5y = 12, find the means of x and y and the correlation coefficient.

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6. 7. a) Derive the characteristic equation of (M/M/1): (∞/FIFO) queuing model and find the average number of customers in the system.

   b) A super market has two girls serving at the counters. The customers arrive in a Poisson fashion at the rate of 12 per hour. Each girl can serve customers at the rate of 7 per hour. Find (i) the probability that an arriving customer has to wait for service (ii) the average number of customers in the system and (iii) the average time spent by a customer in the super-market.

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