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Frequency of Readership	Level of Educational Achievement				Total
	Professional or postgraduates	College graduates	High school grad	Did not complete high school
Never	10	17	11	21	59
Sometimes	12	23	8

		Quarterly output of a Factory
Year	I	II	III	IV
2010	65	58	56	61
2011	68	63	63	67
2012	70	59	56	52
2013	60	55	51	58

i) What is the probability that the mean length of service times is more than and equal to 12 minutes.
ii) Find the 99% confidence interval for the standard deviation of the mean length of service times.

State whether the following statements are true or false and also give the reason in support of your answer:

b) In cluster sampling the variance within clusters is greater than the variance between
clusters.
c) While analysing the data of a 5 × 5 Latin Square design the error d.f. is equal to 12.
d) In a Two way analysis of variance with 4 blocks & 4 treatments the degree of freedom
for the total variation is 15.
e) Suppose a random number generated by Middle. Square Method is 16, then the next
random number will be 44.

A hospital specialises in heart surgery. During the year 2018-19, 2000 patients were admitted for treatment. Average payment made by a patient was Rs. 120000 with a standard deviation of Rs 25000. Assuming the distribution of payments to normal, find:

i) The number of patients who paid between Rs. 1,00,000 and Rs. 1,75,000.

ii) The probability that a patient’s bill exceeds Rs. 75,000

iii) The maximum amount paid by the lowest paying one-third patient.

The telephone department will install a second booth when convinced that an arrival would expect waiting for at least 3 minutes for phone call. By how much should the flow of arrivals increases in order to justify a second booth?

The annual sales revenue (in lakhs of Rs) of a product as a function of sales force (number of salesmen) and annual adverting expenditure (in Thousands of Rs) for the past 10 years are summarised in following table:

Annual Sales Revenue Y(in Lakhs)	Sales Force X1 (in Number)	Annual Advertising Expenditure X2 (in Thousand)
100   115   125   135   105   145   110   120   135   175	40   65   40   90   115   80   50   60   70   100	140   115   190   80   100   140   115   150   130   160

Obtain a regression model to forecast the annual sales revenue of the product using Matrix Method.