Probability and Statistics — CAST202 (3rd Sem)

<P ° e ° ail = Tribhuvan University x OY Faculty of Humanities & Social Sciences LIER a OFFICE OF THE DEAN y 2021 Bachelor in Computer Applications Full Marks: 60 Course Title: Probability and Statistics Pass Marks: 24 Code No: CAST202 Time: 3 hours Semester: III Batch: 2020 Candidates are required to answer the questions in their own words as far as possible. Group B Attempt any SIX questions. [6x5 = 30] 2. Differentiate between Convenient sampling and Systematic random sampling with suitable examples. _3< From the following data, find Mean and Median. Then use an empirical relation across mean, median and mode to find Mode. Age-group 10-20 | 20-30 | 30-40 | 40-50 | 50-60 Number of months (f) BS 175 eel 2 9 a Mean is 34.69 for 65 total observations, find the missing frequency from the following data: Expense-class in thousands rupees 10-20 | 20-30 | 30-40 | 40-50 | 50-60 Number of five-star hotels establishments Ho 1 ae a 10 v. ak Use Karl Pearson's correlation method to examine the relationship between marks obtained in two subjects: | Students | A|B/C|}D/E/F|GIH|I|4J | Statistics | 42 | 51! 65 | 57 | 56 | 28 | 19 | 24 | 33 | 80 Mathematics | 42 | 61 | 66 | 54 | 57 | 28 | 29 P2135 187 | 6. The number of defective articles is found to be 2% in a lot of 300 sample articles per day, then find out following probabilities using suitable probability distribution that (i) There are exactly two defective articles per day (b) there are at least 2 defective articles ‘per day. 7. Six coins are tossed 500 times such that probability of getting a head is 21% in each toss. Fit a Binomial distribution for a number of heads with the following frequency distribution: x] oft [2] 3 [4 | s | 6 [tom] Fe [ies [xo 7055 [as [50 35] 50 8. Ina Hospital, the height of patients follows normal distribution with mean height of 53 inches with standard deviation of 3 inches. Then find out the following probabilities of heights of patients that i) less than 57 inches, il) more than 64 inches, iii) between 50 and 56 inches. Use Normal table.  Group C Pat any TWO questions. [2x10 = 20] . Automobile Company Sells Cars of different model during a year. Data are presented in the following table. ‘Prices of Cars in lakhs) | 12 | 13 | 40 | 15 | 16 | 70 | 80 | 90 |.15 Now, fit a linear regression model of demand of cars. Interpret the intercept and slope of the model Also, find the demand of cars when price is 25 lakhs. Also, find the coefficient of determination and interpret it. 10. An analysis of daily wages, paid to workers in two firms A and B belonging to the same industry, gives the following results. Year | Firm A | Firm B | Number of workers (n) ni=200 | n2=300 Variance of distribution of wages | Rs. 67 | Rs. 86 a) Which firm A or B has a larger wage bill? b) In which firm, A or B, is there a greater consistency or uniformity or variability in individual wages? c) Find out the combined average of both firms A and B. 11 Perform a one-way ANOVA to differentiate average sales of computers from three electronic ee shops as given below at 5% level of significance: Shop A | 10 % [shop B | 3 | Shop C 45 67 78 78 90 Which shop has a greater averages sale of computers? Use F table for Frab (2, 12) at 5%.