Word Count : 340

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Sample No.	Defective pumps
1	5
2	6
3	3
4	2
5	1
6	0
7	4
8	8
9	2
10	2
11	6
12	1
13	10
14	2

Strata	Ni	Ni	Si
1	80	29	12	80
2	160	39	8	30
3	260	32	4	10
	500	100

 

If X₁, X₂, X₃, X₄ and X₅ is a random sample of size 5 taken from anExponential distribution, then estimator T1 is more efficient than T₂.

 

Solve the following LPP using graphical method:

Maximize Z = 3x₁ + 2x₂

Subject to the Constraints:

-2x₁ + x₂ ≤ 1

x₁ ≤ 2

x₁ + x₂ ≤ 3

x1, x₂ ≥0

The menstrual cycle in woman following normal distribution has a mean of 28 days and S.D. of 2 days. How frequently would you expect a menstrual cycle of

i) More than 30 days ii) Less than 22 days

(a) Twenty pieces of different length of cloth contained 2, 4, 1, 3, 5, 4, 2, 7, 3, 5, 2, 2, 4, 5, 6, 4, 2, 1, 2, 4 defectsrespectively. To check the process is under control with respect to the number of defects, we should use p-chart.

(b) If density function of the time to failure of an appliance is   

then reliability of the appliance for two years will be 0.444.

(c) If the probabilities are associated with the occurrence of different states of nature, then the situation is known as decision making under uncertainty.

(d) If there are 1% defectives notes of Rs.500 in a lot of 10000 notes of Rs 500, then the lot quality will be 99%.

(e) A system has four components connected in parallel configuration with reliability 0.2, 0.5, 0.4, 0.6. To improve the reliability of the system, we have to replace the weakest component to the more reliable component.