Monthly rates of return on the shares of a particular common stock are independent of one another and normally distributed with a standard deviation of 1 7 A sample of 12 months is taken a Find the probability that the sample standard deviation is less than 2 7 b Find the probability that the sample standard deviation is more than 0 9 Upper critical values for the chi square distribution X Lower critical values for the chi square distribution X Click the icon to view a table of lower critical values for the chi square distribution Click the icon to view a table of upper critical values for the chi square distribution PROBABILITY OF EXCEEDING THE CRITICAL VALUE PROBABILITY OF EXCEEDING THE CRITICAL VALUE 0 10 0 05 0 025 0 01 0 001 0 90 0 95 975 0 99 0 999 2 706 3 84 5 024 6 635 10 828 016 004 001 000 000 a The probability is 4 605 5 991 7 378 9 210 13 816 211 103 051 020 002 6 251 7 815 9 348 11 345 16 266 584 352 216 115 024 b The probability is 7 779 9 488 11 143 13 27 18 467 1 064 711 484 297 091 DOVaUAWNE 9 236 11 070 12 833 15 086 20 515 1 610 1 145 831 554 210 less than 0 90 10 645 12 592 14 449 16 812 22 458 2 204 1 635 1 237 872 381 2 833 2 167 1 690 1 239 598 12 017 14 067 16 013 18 475 24 322 3 490 2 733 2 180 1 646 857 between 0 95 and 0 975 13 362 15 507 17 535 20 090 26 125 4 168 3 325 2 700 2 088 1 152 14 684 16 919 19 023 21 666 27 877 10 4 865 3 940 3 247 2 558 1 479 between 0 90 and 0 95 15 987 18 307 20 483 23 209 29 588 11 5 578 4 575 3 816 3 053 1 834 17 275 19 675 21 920 24 725 31 264 12 6 304 5 226 4 404 3 571 2 214 between 0 99 and 0 999 18 549 21 026 23 337 26 217 32 910 13 7 042 5 892 5 009 4 107 2 617 19 812 22 362 24 736 27 688 34 528 14 7 790 6 571 5 629 4 660 3 041 greater than 0 999 21 064 23 685 26 119 29 141 36 123 15 8 547 7 261 6 262 5 22 3 483 15 22 307 24 996 27 488 16 30 578 37 697 9 312 7 962 6 908 5 812 3 942 between 0 975 and 0 99 16 23 542 17 26 296 32 000 39 252 10 085 8 672 7 564 6 408 28 845 4 416 18 10 865 9 390 8 231 7 015 4 905 17 24 769 27 587 30 191 33 409 40 790 19 11 651 10 117 8 907 7 633 5 407 25 989 28 869 31 526 34 805 42 312 12 443 10 851 9 591 8 260 5 921 19 27 204 30 144 32 852 36 191 43 820 13 240 11 59 10 283 8 897 6 447 20 28 412 31 410 34 170 37 566 45 315 14 041 12 338 10 982 9 542 6 983 29 615 32 671 35 479 38 932 46 797 14 848 13 091 1 689 10 196 7 529 30 813 33 924 36 781 40 289 48 268 15 659 13 848 12 401 10 856 8 085 32 007 35 172 38 076 41 638 49 728 16 473 14 611 13 120 11 524 8 649 33 196 36 415 39 364 42 980 51 179 15 379 13 844 12 198 9 222 9 803 34 382 14 573 12 879 37 652 40 646 44 314 18 114 16 151 52 620 35 563 18 939 16 928 15 308 13 565 38 885 41 923 10 391 45 642 54 052 19 768 17 708 16 047 14 256 10 986 36 741 40 113 13 195 46 963 55 476 30 20 59 18 493 16 791 14 953 11 58 37 916 41 337 44 461 48 278 56 892 40 29 051 26 509 24 433 22 164 17 916 39 087 42 557 45 722 49 588 58 301 50 37 689 34 764 32 357 29 707 24 674 40 256 43 773 16 979 50 892 59 703 60 46 459 43 188 10 482 37 485 31 738 51 805 55 758 59 342 63 691 73 402 70 55 329 51 739 18 758 45 442 39 036 63 167 67 505 71 420 76 154 86 661 80 64 278 60 391 57 153 53 540 46 520 74 397 79 082 83 298 88 379 99 607 90 73 291 69 126 65 647 61 754 54 155 70 85 527 100 90 531 95 023 100 425 112 317 82 358 77 929 74 222 70 065 61 918 96 578 101 879 106 629 112 329 124 839 0 90 0 95 0 975 0 99 0 999 107 565 113 145 118 136 124 116 137 208 Print Done Print Done

Question

Monthly rates of return on the shares of a particular common stock are independent of one another and normally distributed with a standard deviation of 1 7  A sample of 12 months is taken  a  Find the probability that the sample standard deviation is less than 2 7  b  Find the probability that the sample standard deviation is more than 0 9  Upper critical values for the chi square distribution    X Lower critical values for the chi square distribution  X Click the icon to view a table of lower critical values for the chi square distribution  Click the icon to view a table of upper critical values for the chi square distribution  PROBABILITY OF EXCEEDING THE CRITICAL VALUE PROBABILITY OF EXCEEDING THE CRITICAL VALUE 0 10 0 05 0 025 0 01 0 001 0 90 0 95  975 0 99 0 999 2 706 3 84 5 024 6 635 10 828  016  004  001  000  000 a  The probability is 4 605 5 991 7 378 9 210 13 816 211  103  051  020  002 6 251 7 815 9 348 11 345 16 266 584  352 216  115  024 b  The probability is 7 779 9 488 11 143 13 27 18 467 1 064  711 484  297  091 DOVaUAWNE 9 236 11 070 12 833 15 086 20 515 1 610 1 145 831  554  210 less than 0 90  10 645 12 592 14 449 16 812 22 458 2 204 1 635 1 237 872 381 2 833 2 167 1 690 1 239 598 12 017 14 067 16 013 18 475 24 322 3 490 2 733 2 180 1 646  857 between 0 95 and 0 975  13 362 15 507 17 535 20 090 26 125 4 168 3 325 2 700 2 088 1 152 14 684 16 919 19 023 21 666 27 877 10 4 865 3 940 3 247 2 558 1 479 between 0 90 and 0 95  15 987 18 307 20 483 23 209 29 588 11 5 578 4 575 3 816 3 053 1 834 17 275 19 675 21 920 24 725 31 264 12 6 304 5 226 4 404 3 571 2 214 between 0 99 and 0 999  18 549 21 026 23 337 26 217 32 910 13 7 042 5 892 5 009 4 107 2 617 19 812 22 362 24 736 27 688 34 528 14 7 790 6 571 5 629 4 660 3 041 greater than 0 999  21 064 23 685 26 119 29 141 36 123 15 8 547 7 261 6 262 5 22 3 483 15 22 307 24 996 27 488 16 30 578 37 697 9 312 7 962 6 908 5 812 3 942 between 0 975 and 0 99  16 23 542 17 26 296 32 000 39 252 10 085 8 672 7 564 6 408 28 845 4 416 18 10 865 9 390 8 231 7 015 4 905 17 24 769 27 587 30 191 33 409 40 790 19 11 651 10 117 8 907 7 633 5 407 25 989 28 869 31 526 34 805 42 312 12 443 10 851 9 591 8 260 5 921 19 27 204 30 144 32 852 36 191 43 820 13 240 11 59 10 283 8 897 6 447 20 28 412 31 410 34 170 37 566 45 315 14 041 12 338 10 982 9 542 6 983 29 615 32 671 35 479 38 932 46 797 14 848 13 091 1 689 10 196 7 529 30 813 33 924 36 781 40 289 48 268 15 659 13 848 12 401 10 856 8 085 32 007 35 172 38 076 41 638 49 728 16 473 14 611 13 120 11 524 8 649 33 196 36 415 39 364 42 980 51 179 15 379 13 844 12 198 9 222 9 803 34 382 14 573 12 879 37 652 40 646 44 314 18 114 16 151 52 620 35 563 18 939 16 928 15 308 13 565 38 885 41 923 10 391 45 642 54 052 19 768 17 708 16 047 14 256 10 986 36 741 40 113 13 195 46 963 55 476 30 20 59 18 493 16 791 14 953 11 58 37 916 41 337 44 461 48 278 56 892 40 29 051 26 509 24 433 22 164 17 916 39 087 42 557 45 722 49 588 58 301 50 37 689 34 764 32 357 29 707 24 674 40 256 43 773 16 979 50 892 59 703 60 46 459 43 188 10 482 37 485 31 738 51 805 55 758 59 342 63 691 73 402 70 55 329 51 739 18 758 45 442 39 036 63 167 67 505 71 420 76 154 86 661 80 64 278 60 391 57 153 53 540 46 520 74 397 79 082 83 298 88 379 99 607 90 73 291 69 126 65 647 61 754 54 155 70 85 527 100 90 531 95 023 100 425 112 317 82 358 77 929 74 222 70 065 61 918 96 578 101 879 106 629 112 329 124 839 0 90 0 95 0 975 0 99 0 999 107 565 113 145 118 136 124 116 137 208 Print Done Print Done

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