1000 light bulbs with a mean life of 120 days are installed in a new factory and their length of life is normally distributed with standard deviation of 20 days.

 (i) How many bulbs will expire in less than 90 days?

(ii) If it is decided to replace all the bulbs together, what interval should be allowed between replacements if not more than 10% should expire before replacement?

Use the Jacobi method to solve the following system of equations: 
3x + 4y + 15z = 54.8
x + 12y + 3z = 39.66
10x + y — 2z = 7.74

Calculate the value of the integral

(i) Simpson's 1/3 rule,

(ii) Simpson's 3/8 rule.

Briefly discuss the following with a suitable example:

(i) Non Linear Regression

(ii) Acceptance Rejection method

What are residual plots? Discuss the utility and disadvantage of residual plots.

The length of metallic strips produced by a machine has mean 100 cm and variance 2.25 cm. Only strips with length between 98 and 103 cm are acceptable. What proportion of strips will be acceptable? You may assume that the length of a strip has a Normal Distribution.

Solve the following system of equations by using the Gauss Elimination method: (8 Marks)
 x + 2y + z = 3
2x + 3y + 3z = 10
3x y + 2z = 13

In the table below, the value of y are consecutive terms of a series of which 23.6 is the sixth term. Find the first and tenth terms of the series using Newton’s forward interpolation method.