Page 1 : MODEL PAPER - 2022, II PUC, SUBJECT: STATISTICS (31), [Total No. of questions: 55], Time: 3Hrs.15Mins. Max. Marks: 100, , , , Il., , 16., ie, 18., 19., 20., , 21., 22., 23., , 24., 25., 26., 27., , Note: 1. Statistical table and graph sheets will be supplied on request., 2. Scientific calculators may be used., 3. All working steps should be clearly shown., , Section -A, Answer anyten of the following questions. 10x 1=10, Define fecundity., Define life table., Name the index number which does not satisfy unit test., Define consumer price index number., What is Historigram?, Which variation of the time series is unpredictable?, Write the parameter of a Bernoulli distribution., What is the total area under the normal curve?, , For a chi square (x?) variate, isp < x2 < 13.33)= 0.5, find median., , What is meant by estimation?, Define null hypothesis., Define confidence interval., What is a control chart?, , In L.P.P define solution., , Define ‘strategy’ in a game., , Section -B, Answer anyten of the following questions. 10x 2=20, Mention two uses of vital statistics., In a life table, if l= 95,400 and lz = 93,492 then, find di., Mention two characteristics of index numbers., If Upiq = 450 and Zpoq= 400, find Kelly’s price index number., Find consumer price index number from the following data., , , , , , , , , , Group A B Cc D, Group Index | 100 | 120 | 130 | 110, Weight 2 3 1 4, , , , , , , , , , , , , , Mention two uses of time series., , Diagrammatically represent ‘Business Cycle’ with stages., , Write down the conditions for applying of Binomial expansion method of, interpolation and extrapolation., , Find P(X = 0) in a Poisson distribution with mean 5., , If n = 4 for student’s t-distribution, find S.D., , If P= 0.1 and n = 100, then find S.E(p)., , Define type I and type II errors., , Page |1, , Scanned with CamScanner

Page 2 : 28., 29., 30., , Il., , 31., , 32., , 33., , 34., , 35., , 36., , 37., , If X= 40, R=2.5 and Ae= 0.577, find lower control limit of X- chart., What are degenerate and non-degenerate solutions in T.P?, , Mention two needs for replacement of equipments., , Section - C, Answer any eight of the following questions., From the following data, find CBR and GFR., , 8x5=40, , , , , , , , , , , , , , , , , , , , Age [in Male Female Number of live, years| Population Population births, O-14 46000 43000 15 - 24 34000 32000 6846, 25 - 39 39000 38000 3893, 40 - 49 30000 28000 674, 50 - 79 27000 26000 80 & above 15000 12000 , , , , , , , For the following data, calculate gross reproduction rate., , , , , , , , , , , , , , , , , , , , , , , , Age group | 15_19 | 20-24 | 25-29 | 30-34 | 35-39 | 40-44 | 45-49, [in years], , Female | 14,000 | 15,000 | 14,000 | 13,000 | 12,000 | 11,000 | 10,000, population, , Female 630 870 980 650 600 220 30, , births, , , , What are the steps involved in the construction of index number? Explain any, , two of them., , The following are the prices (in Rs.) of items in 2010 and 2015. Find simple, geometric mean price index number., , , , , , , , , , , , , , , , Ttem A |B ]cCc{|D{ F, Price| 2010 | 50 | 60 | 20 | 50 | 80 | 125, (Rs) [2015 | 55 | 75 | 30 | 75 | 70 | 130, , , , , , , , Obtain trend values by 3 yearly moving averages for the following data., , , , , , , , , , , , , , , , , , , , , , , , Year | 1995 | 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 2004, Sales, (000) 86 63 45 58 43 57 98 120 100 150, , , , , , , , Year, , 2002, , 2004, , 2006 | 2008, , 2010 | 2012, , , , , , Profit (in crores), , 10, , , , 20, , , , 32 |, , 36, , , , , , , , 52 60, , , , For the following time series fit a linear trend by the method of least squares., , Interpolate and extrapolate the production for the years 2000 and 2010 with, the help of the following table., , , , Year, , 1980, , 1985, , 1990, , 1995, , 2000 | 2005, , 2010, , , , , , Production (tons), , , , 5, , , , 12, , 19, , , , , , 26, , 3 40, , , , , , , , , , , , Scanned with CamScanner, , Page | 2

Page 3 : 38., , 39., , 40., , 41., , 42., , 43., , 44,, , 45., , In a city 40% of the people are vegetarians. In a random sample of 6 persons, find the probability that i) 3 are vegetarians, ii) at least one is vegetarian., , A pond has 10 fishes among which 4 are marked ones (marked fishes are, under scientific observation). 4 fishes are caught from the pond. Find the, probability that two of them are marked ones. Also find the mean of marked, ones., , It is required to test whether those who practice Yoga have average blood, sugar less than 120 mg/dl. A sample consisting of 36 persons who practice, Yoga is observed. If their mean blood sugar is 118.5 mg/dl and variance is 9, mg2/dl. At 1% level of significance what would you conclude?, , For the following data examine whether the means differ significantly? Use, a=0.05., , , , , , , , , , , , , , , , Sample I II, Size 12 7, Mean 57.2 52.3, S.D. 3.41 3.62, , , , , , From the following data, test whether ‘education’ and ‘employment’ are, independent at 1% level of significance., , , , , , , , , , . Employment, Education Employed | Unemployed, Educated 20 25, Uneducated 15 40, , , , , , , , , , , , In a floor mat manufacturing company, the average number of defects per, square meter is known to be 4. Determine the control limits for the number of, defects., , Solve the following L.P.P graphically:, Max. Z = 10x + 15y, s.t.x+y<s10, 3x+2y 215, and x, y20, OR, (For visually challenged students only), Explain graphical method of solving L.P.P., , Solve the following game using the principle of dominance., , Page |3, , Scanned with CamScanner

Page 4 : Player B, , B; B, B,, , Ajfl 2 0, , Player A A,]}4 6 3, A,\3 -1 -2, , 4, , 3, 5, 0, , Section -D, , IV. Answer any two of the following questions., , 46., , 47., , 48., , 49., , 50., , 2x 10=20, From the following data, compute standardized death rates for Town A and, Town B. Comment on the results., , , , , , , , , , , , , , , , , , , , , , , , Age group | Town - A Town -B Standard, [in years] | Population | Deaths | Population | Deaths | Population, 0-20 | 4,000 36 3,000 30 2,000, 20-40 | 12,000 48 20,000 100 3,000, 40-60 | 6,000 60 4,000 48 6,000, , 60 & above | 8,000 152 3,000 60 4,000, , , , , , following data., , , , , , , , , , , , , , , , , , Item _ 2004 2008 :, Price (Rs.) | Quantity | Price (Rs.) | Quantity, A 10 5 15 4, B 15 8 20 t, Cc 6 3 10 5, D 3 4 4 5, , , , , , , , , , , , , , , , , , , , , , , , FRT., Tet Price (Rs.) Quantity, Base year | Current year | Base year | Current year, A 4 6 4 6, B 6 10 4 8, Cc 8 11 5 3, , , , , , , , , , , , Year 2005, , 2007 | 2008 | 2009, , , , 10, , , , , , Profit (in lakhs), , 8, , 12 18 26, , , , , , , , , , Following is the data regarding n, Fit a Poisson distribution. Test at 5% L.O.S. that it is a good fit., , , , , , , , , , , , , , , , , , , , , , , , Find Laspeyre’s, Paasche’s and Dorbish-Bowley’s price index numbers for the, , For the following data verify whether Fisher’s index number satisfies TRT and, , For the following time series fit a second degree trend of the type Y = a + bx + cx?, by the method of least squares. Estimate the profit for the year 2010., 2006, , umber of mistakes per page found in a book., , No. of mistakes per page | 0 1 2 3 4 5 and more, No. of pages 31 | 34 | 21 | 12 2 0, Section - E, Answer any two of the following questions. 2x5=10, , Scanned with CamScanner, , Page | 4

Page 5 : 51., , 52., , 53., , 54., , 55., , Marks scored by the students of a class follows normal distribution with, mean 80 and S.D. 5. Find the probability that a student selected at random, from the class scored i) more than 70 marks ii) between 75 and 90 marks., , In a random sample of 120 people from a city in the year 2011 revealed that, 96 were cricket match viewers. In another random sample of 100 people from, same city in the year 2013 revealed that 90 were cricket match viewers., Examine whether there is a significant increase in the proportion of cricket, match viewers. Use 1% level of significance., The following data represents the blood pressure of 5 persons before and after, performing dhyana:, Person A B Cc D E, B.P. Before Dhyana | 90 | 90 | 100] 88 | 99, B.P. After Dhyana 88 | 90 | 95 | 90 | 96, Can we conclude at 5% level of significance that Dhyana reduces blood, pressure?, , , , , , , , , , , , , , , , , , , , , , , , The purchase price of a machine is Rs 8,000. Its maintenance costs and, resale values are given below:, , , , , , , , , , Year 1 2 3 4 5, Maintenance cost (Rs.) | 500 | 600 | 800 | 1,100] 1,500, Resale value (Rs.) 4,500 | 3,500 | 2,500} 1,500} 500, , , , , , , , , , , , , , , , What would be the optimum replacement period of machine? What would be, the average annual cost?, , There is a demand for 10,000 items per year. The replenishment cost is, Rs.200 and the maintenance cost is Rs.9 per item per year. Replenishment is, instantaneous and shortages are not allowed. Find economic order quantity, , and minimum average inventory cost., tek, , Page [5, , Scanned with CamScanner