(7 pages) APRIL 2013 12. What is the difference between small sample and large sample? Answer any TEN questions each in 50 words. All qu~tions carry equal marks. 4. Defineprol;Jability. 13. A retailer purchases berries every· morning at Rs. 5 a case and sells for Rs. 8 a case. Any case remaining unsold at the end of the day can be disposedof next day at a salvage value of Rs. 2 per case (thereafter they have no value). Past sales have ranged from 15 to 18 cases per day. The folloWing is the record of sales for Past 120 day: Cases sold: 15 16 17 18 No~of days: 12 24 48 36 Find how many cases the retailer should purchase Per day to maximise his pmfit. 14. 15. 16. Three groups of workers contain 3 men and one woman, 2 men and 2 women, and 1 man and three women respectively. One worker is selected at random from each group. What is the probability that the group selected consist of 1 man and 2 women? regulators, r12= 0.70; rta = 0.61; 1'28= 0.40. assembly electrical of which is being space and finance, the number of workers employed cannot exceed 11 and their salary bill not more than Rs. 6000 per month. The. male members ()f the skilled workers are paid Rs. 600 per month, while the female worker, doing the same work as the male member gets Rs. 500 per month. Data collected on the performance of these workers indicate that a male member contributes Rs. 1000 per month to total return of the industry, A random sample of size 16 has 53 as mean. The sum of the squares of the deviations taken from mean is 135. Can this ~ple be regarded as taken from the ,population having 56 as mean? Obtain 95% and 99% confidence limits of the mean of the population. On the basis of the following information compute: (a) 1'28.1 (b) rl3.2and (c) rt2.8: the manufactures accomplished by a small group of skilled workers, both men and women .. Due to the limitations of Assuming that half the population is vegetari.all so that the chance of an individual being a vegetarian IS ~ and assuming that 100 investigators can take sample of 10 Individuals to see whether they are vegetarians, how many investigators would you expect to report that three people or less were vegetarians? (for v = 15, to.05= 2.13 for v = 15, to.Ol= 2.95). 17. 18. A small scale industry while the female worker contributes' Rs. 850 per month. Formulate the LPP to determine the number of male and female workers to be employed in order to maximize the monthly total return. 19. Assume the mean height of soldiers to be 68.22 inches with a variance of 10.8 inches. How mapy soldiers in a regiment of 1,000 would you expect is being over six feet tall? 6S1071KCA2B [p.T.O.] Calculate the Karl Pearson's coefficient of correlation from the followingdata and interpret its value: Marks in Accountancy: 48 35 17 23 47 Marks in Statistics: 45 20 40 25 45 The customer accounts at a certain departmental store have an average balance of Rs. 480 and a standard deviation of Rs. 160. Assuming that the account balances are normally distributed. (a) What proportion of· the accounts is over Re.OOO? (b) What proportion of the accounts is between Rs. 400 and Rs. 6OO? (c) What proportion of the accounts is between Re. 240 and Rs. 360? A manufacturing company has purchased three new machines of different makes and wishes to determine whether one of them is faster than the others in producing a certain output. Five hourly production figures are observed at random from each machine and the results are given below: 1 25 31 24 2 30 39 30 3 36 38 28 Use the analysis of variance and determine whether the machines are significantly different. in their mean speed. (Given at 5% Level F2.12 = 3.89). 25. Eight coins are tossed at a time 25_6times. Number of heads observed at each throw is recorded and the results are given below.Find the expected frequencies. What are the theoretical values of mean and standard deviation? Calculate also the mean and S.D.of the frequencies. No. of heads at a throw: 0 1 2 3 4 5 ~. 7 8 Frequency : 2 6 30 52 67 56 32 10 1