A husband and wife appear in an interview for two vacancies in the same post. The probability of husband’s selection is 18 and that of wife’s selection is ¼. What is the probability that:
(i) Both of them will be selected
(ii) Only one of them will be selected
(iii) None of them will be selected.

 

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

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

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?

A husband and wife appear in an interview for two vacancies in the same post. The probability of husband’s selection is 18 and that of wife’s selection is ¼. What is the probability that:
(i) Both of them will be selected
(ii) Only one of them will be selected
(iii) None of them will be selected.

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.