Calculate the following using the data in Table 9.3.

a. The total number of deaths between ages 60 and 65.

b. The probability that a life aged 56 exact will survive to age 80 exact.

c. The probability that a life currently aged 10 exact will die between his 50th and 55th birthdays.

d. The probability that a new-born will die aged 81.

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Table 9.3 Illustrative life table dx lx lx dx 0 100,000 814 21 98,413 85 42 96,155 194 63 82,701 1625 1 87 43 95,961 210 64 81,076 1783 2 99,186 62 22 99,124 38 23 99,086 30 24 95,751 230 65 79,293 1940 98,328 98,241 87 44 98,154 87 45 98,067 84 46 3 95,521 255 66 77,353 2097 4 24 25 95,266 283 67 75,256 2255 99,056 99,032 22 26 5 97,983 83 47 94,983 315 68 73,001 2403 6 352 69 70,598 7 391 70 68,055 8 436 71 65,381 9 485 72 62,562 59,593 56,484 53,266 99,010 20 27 97,900 83 48 94,668 98,990 18 28 97,817 85 49 94,316 98,972 19 29 97,732 87 50 93,925 98,953 18 30 97,645 89 51 93,489 98,935 18 31 97,556 91 52 93,004 537 73 98,917 18 32 97,465 95 53 92,467 594 74 98,899 19 33 97,370 97 54 91,873 656 75 98,880 23 34 97,273 103 55 91,217 727 76 97,170 113 56 90,490 806 77 97,057 124 57 89,684 892 96,933 133 58 88,792 987 79 96,800 145 59 87,805 1091 80 96,655 155 60 86,714 1207 81 96,500 166 61 85,507 1334 82 96,334 179 62 84,173 1472 49,965 98,857 29 35 46,579 98,828 39 36 78 43,124 98,789 52 37 39,630 98,737 74 38 36,128 32,654 98,663 86 39 98,577 81 40 83 41 29,254 98,496 10 11 12 13 14 15 16 17 18 19 20 x lx dx X dx X 2543 2674 2819 2969 3109 3218 3301 3386 3455 3494 3502 3474 3400 3300 Notes: The table is actually based on the mortality of the male population of Britain in the early 1990s and is an extract of the English Life Tables No. 15 published by the Stationary Office.