PFA

PFA


Assignment 1 Predictive AnalyticsFull Marks 20 [4 x 5 = 20] 1. Using MS-Excel answer the following questions and plot the relevant probability distribution functions (PMF and CDF) a) On average, 20 customers per day cancel their order placed at Fashion Trends Online. Calculate the probability that the number of cancellations on a day is exactly 20. b) Fashion Trends Online (FTO) is an e-commerce company that sells women apparel. It is observed that about 10% of their customers return the items purchased by them for many reasons. On a particular day, 20 customers purchased items from FTO. Calculate the probability that a maximum of 5 customers will return the items. 2. A manufacturer of sports equipment has developed a new synthetic fishing line that the company claims has a mean breaking strength of 8 kilograms. A random sample of 50 lines is tested and their breaking strengths have been recorded in the file fishing_line.xlsx. Use a 0.01 level of significance and test if the claim is supported by data. Show relevant calculations and use of formula using MS-Excel. 3. Using MS-Excel answer the following questions and plot the relevant probability distribution functions (PMF and CDF) a) Health First hospital recruits nurses frequently to manage high attrition rate. It was estimated that only 70% of offers rolled out by the hospital are accepted. If 10 offers are made, what is the probability that at least 8 candidates will accept the offer from the hospital? b) The number of calls arriving at a call center follows a Poisson distribution at 10 per hour. Calculate the probability that the number of calls over a 1-hour period will exceed 15. 4. A passport office claims that the passport applications are processed within 30 days of submitting the application form and all necessary documents. Passport.xlsx provides the processing time in days for 40 passport applicants. From experience it was found that the standard deviation of the processing time is 12.5 days. Conduct a hypothesis test at significance level a = 0.05 to verify the claim made by the passport office. Show relevant calculations and use of formula using MS-Excel. Sheet1 Sl No.Processing Time 116 216 330 437 525 622 719 835 927 1032 1134 1228 1324 1435 1524 1621 1732 1829 1924 2035 2128 2229 2318 2431 2528 2633 2732 2824 2925 3022 3121 3227 3341 3423 3523 3616 3724 3838 3926 4028 Sheet1 Sl No.Breaking Strength 16.7 27.9 38.1 47.7 58.9 67.2 78.6 89.2 97.5 108.3 118.0 126.8 137.3 147.2 158.5 167.9 178.6 188.7 198.7 208.1 217.8 227.1 236.8 247.2 257.6 267.9 278.4 288.5 298.2 307.8 317.6 327.6 337.6 347.2 357.1 368.0 377.7 388.1 397.9 408.5 418.2 428.2 437.8 447.5 458.1 468.4 477.6 487.2 498.3 507.4