**PART 1**

(2) (b) Given thatis a probability distribution. Find k.

2. Derive mean of a binomial distribution.

3. During one stage in the manufacture of integral circuit chips a coating must be applied. If 70% chips receive a thick enough coating, find probabilities that among 15 chips

(a) atleast 12 will have thick enough coating.

(b) atmost 6 will have thick enough coating.

(c) exactly 10 will have thick enough coating.

4. Find the positive solution of 2sinx=x using Newton-Raphson method.

5. Use Newton-Raphson method to find a root of the equation x^3-2x-5=0.

6. (a) Given f(2)=9 and f(6)=17. Find an approximate value of f(5) by linear Lagrange’s interpolation.

(b) Compute an approximate value of ln 9.2 correct to 4 decimal places from ln 9.0=2.1972 and ln 9.5=2.2513 by linear Lagrange interpolation.

**Part 2**

2. Find mean and Variance for the following probability distribution:

3. If the probability is 0.05 that a certain wide-flange column will fail under a given axial load, what are the probabilities that among 16 such columns,

i) At most 2 will fail

ii) At least 4 will fail

4. Design a Newton’s-Raphson formula to find cube root of a given positive number and apply it for C = 7, X0 = 2.

5. Apply Newton-Raphson Method to the equation f(x ) = x^3+ x− 1 = 0, (Four Iteration).

6. State the conditions for Poisson approximation to Binomial distribution. Approximate
Binomial distribution as Poisson .

OR

7. i) The probability that a person suffers bad reaction due to a certain injection is 0.001.

Determine out of 2000 individuals, the probability of exactly 3 will suffer the bad reaction and probability of more than 2 will suffer bad reaction.

ii) The probability that a bomb dropped from a plane will hit the target is 1/5. If 6 bombs are dropped , find the probability of exactly 2 will strike the target and probability of at least 2 will strike the target.

8.Given f(32) = 0.5299, f(35) = 0.5736, f(38) = 0.6157, f(41) = 0.6561, f(44) = 0.6947. Find f(42) and f(43) using Interpolation.

9. Using Langrange’s formula, fit a polynomial for the following data.

x:1 2 7 8

y:4 5 5 4

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