Using the Hours worked per week data:

1. Calculate the mean and (sample) standard deviation of these data.
2. Now, assume you select an individual from a normally distributed population with mean and standard deviation corresponding to your values in a above (i.e. use them as and .What is the probability that this person works more than 35 hours per week?What is the probability they work less than 15 hours per week?What is the probability they work between 20 and 30 hours per week?For each of these probabilities, give also the Excel command you've used to obtain them.
3. Again, assuming the population of Hours worked is normally distributed, what is the 80th percentile of this distribution?Give the Excel command you use to obtain this percentile.
4. Comment on the likely validity of the normal distribution in this case.Include graphs to support your claim.

Gender Age Ethnicity Marital Qualification PostSchool Hours Income Female 21 Maori Never School No 2 11 Female 41 European Married Vocational Yes 17 18 Female 21 European Never School No 6 18 Female 22 European Never School No 6 24 Male 18 Maori Never School No 5 44 Male 18 Maori Never School No 4 44 Female 17 Maori Never School No 4 62 Female 20 European Never School No 12 74 Female 19 European Never None No 3 94 Female 18 Pacific Other School No 9 102 Female 16 European Never None No 3 107 Female 16 European Never None No 2 108 Female 31 European Other School No 24 143 Female 15 European Never None No 8 172 Female 15 European Never None No 8 172 Female 15 European Never None No 8 172 Female 15 European Never None No 8 172 Female 36 European Married Vocational Yes 5 193 Female 42 European Married None No 6 201 Female 43 European Married None No 6 206 Female 43 European Married None No 9 218 Female 31 European Previously School No 9 218 Male 17 European Never None No 15 222 Male 17 European Never None No 15 227 Female 19 European Married School No 15 230 Female 18 European Married School No 15 231 Female 16 European Never School No 9 232 Female 16 European Never School No 9 232 Male 18 European Never None No 14 239 Male 18 European Never None No 14 240 Female 33 Pacific Never School No 17 244 Female 33 Pacific Never School No 17 244 Female 33 Pacific Never School No 17 249 Female 18 European Never School No 17 249 Female 18 European Never School No 17 255 Female 18 European Never School No 17 255 Female 16 European Never School No 20 260 Female 30 European Never School No 19 266 Female 43 European Previously None No 25 266 Female 24 Pacific Married None No 6 287 Female 22 European Never School No 15 309 Female 39 Maori Married School No 16 323 Female 34 European Married School No 24 371 Female 33 European Never Vocational Yes 15 371 Female 33 European Never Vocational Yes 14 371 Male 22 European Never School No 40 371 Male 22 European Never School No 40 375 Female 34 European Married School No 24 375 Female 45 European Married School No 24 383 Female 34 European Other None No 25 386 Female 16 European Never School No 20 386 Female 45 European Married School No 24 386 Female 45 European Married School No 24 392 Male 34 European Never None No 30 395 Female 42 European Married None No 40 402 Female 32 European Married None No 40 406 Female 36 European Married Vocational Yes 24 406 Female 27 Maori Never School No 20 406 Female 32 European Married None No 40 406 Female 27 Maori Never School No 20 406 Female 36 European Married School No 20 409 Female 25 Maori Never Vocational Yes 25 409 Female 32 European Married None No 40 409 Female 40 European Never Degree Yes 13 425 Female 40 European Never Degree Yes 13 425 Male 36 European Married None No 35 426 Female 45 European Never None No 40 426 Female 26 European Married Vocational Yes 42 426 Female 45 European Never None No 40 431 Female 30 European Married Vocational Yes 18 450 Female 30 European Married Vocational Yes 19 450 Female 30 European Married Vocational Yes 18 450 Male 23 European Never Vocational Yes 25 455 Male 22 European Never Vocational Yes 25 455 Male 22 European Never Vocational Yes 25 462 Male 30 European Never Vocational Yes 25 462 Male 23 European Never Vocational Yes 25 462 Female 38 European Married Vocational Yes 32 463 Female 27 European Never None No 40 474 Female 27 European Never None No 40 474 Male 22 European Never School No 44 475 Male 28 European Married None No 54 480 Female 21 European Never School No 35 480 Female 21 European Never School No 34 485 Male 38 Maori Married None No 40 497 Male 33 Maori Married None No 40 497 Male 38 Maori Married None No 40 501 Male 18 Pacific Never None No 35 506 Male 25 European Never School No 40 507 Male 18 Pacific Never None No 35 508 Female 23 Maori Never Vocational Yes 38 515 Male 23 European Never School No 45 515 Female 23 Maori Never Vocational Yes 38 517 Female 23 Maori Never Vocational Yes 38 517 Male 40 Maori Previously Vocational Yes 39 525 Female 42 Other Married Vocational Yes 26 526 Female 34 European Previously Vocational Yes 38 532 Female 34 European Previously Vocational Yes 38 532 Male 37 European Previously School No 50 532 Male 35 European Married School No 40 548 Female 28 European Married Degree Yes 50 548 Female 45 Maori Married None No 40 552 Female 43 European Never None No 40 556 Male 32 European Married Vocational Yes 38 556 Male 45 European Never Vocational Yes 40 564 Female 32 European Married Degree Yes 40 564 Female 34 European Married School No 38 564 Female 32 European Married Degree Yes 40 581 Female 40 European Married Vocational Yes 42 596 Female 40 European Married Vocational Yes 42 596 Female 32 European Married Degree Yes 40 596 Male 44 European Previously None No 45 609 Male 44 European Previously None No 45 609 Male 16 Other Never School No 54 615 Female 19 European Married School No 40 623 Female 18 Maori Never School No 45 628 Female 24 European Never Vocational Yes 40 628 Male 17 European Never School No 40 630 Male 17 European Never School No 40 642 Male 17 European Never School No 40 642 Male 17 European Never School No 40 642 Female 23 Other Never Degree Yes 45 658 Male 40 European Other None No 36 662 Male 35 European Married Vocational Yes 45 662 Male 35 European Married Vocational Yes 45 706 Male 25 European Never Vocational Yes 40 708 Male 25 European Never Vocational Yes 40 710 Female 27 European Other Vocational Yes 38 713 Male 27 Maori Never School No 45 724 Female 45 European Married Vocational Yes 48 746 Female 20 Other Never Vocational Yes 50 746 Male 18 Other Never School No 60 768 Female 16 European Married Vocational Yes 46 768 Female 16 European Married Vocational Yes 45 781 Female 16 European Married Vocational Yes 46 781 Male 40 European Married Vocational Yes 45 781 Male 29 European Married Vocational Yes 37 781 Female 16 European Married Vocational Yes 47 795 Male 29 European Married Vocational Yes 37 795 Female 33 European Married Vocational Yes 48 801 Male 29 European Married Vocational Yes 37 801 Male 26 European Never Degree Yes 38 809 Male 37 European Married Vocational Yes 40 815 Female 30 Maori Never School No 40 819 Female 31 Maori Never School No 40 820 Female 31 Maori Never School No 40 826 Male 34 European Never None No 54 826 Male 38 European Married None No 50 835 Male 34 European Married Vocational Yes 55 835 Male 38 European Married None No 50 849 Male 34 European Married Vocational Yes 55 849 Male 42 European Previously Degree Yes 54 856 Male 41 European Previously Degree Yes 54 856 Male 42 European Previously Degree Yes 54 856 Male 39 European Married None No 54 856 Male 41 European Previously Degree Yes 50 856 Female 21 European Other School No 36 868 Male 21 Maori Never School No 50 868 Male 24 European Never Vocational Yes 54 868 Male 23 European Never Vocational Yes 70 884 Male 22 European Never Vocational Yes 70 884 Male 22 European Never Vocational Yes 65 884 Female 36 European Previously Degree Yes 40 925 Male 45 European Married Vocational Yes 44 927 Male 36 European Other Vocational Yes 40 927 Male 36 European Other Vocational Yes 40 927 Female 36 European Previously Degree Yes 40 927 Male 37 European Married None No 50 949 Male 43 European Married Degree Yes 45 950 Male 27 European Never Vocational Yes 40 952 Male 27 European Never Vocational Yes 40 952 Male 31 European Never School No 50 954 Male 31 European Never School No 50 954 Female 34 European Married Vocational Yes 40 967 Male 31 European Never School No 50 972 Male 31 European Never Degree Yes 40 979 Female 37 European Previously Degree Yes 50 985 Female 38 European Never Vocational Yes 40 1084 Female 38 European Never Vocational Yes 40 1097 Male 18 European Other Vocational Yes 40 1099 Male 34 European Previously Vocational Yes 45 1099 Male 18 European Other Vocational Yes 40 1099 Male 35 European Married School No 70 1131 Male 35 European Married School No 70 1145 Male 41 Other Married Degree Yes 45 1145 Male 20 Other Other Vocational Yes 60 1147 Female 39 European Other Degree Yes 55 1152 Male 22 Maori Never Vocational Yes 70 1152 Male 21 Maori Never Vocational Yes 70 1157 Male 38 Maori Previously Degree Yes 50 1163 Male 34 European Married Vocational Yes 60 1217 Male 38 Maori Previously Degree Yes 50 1217 Male 35 European Married Vocational Yes 60 1373 Female 29 European Never Degree Yes 60 1543 Female 29 European Never Degree Yes 60 1543 Male 45 European Married Degree Yes 50 1614 Male 45 European Married Degree Yes 50 1614 Male 32 European Married Degree Yes 70 1724 Male 26 European Never Degree Yes 50 1724 Male 26 European Never Degree Yes 50 1789