Please help with the attached question :

A certain actuarial model of mortality rate is fitted to some given data. Table 3 below reports the Z- score statistic of the model graduation. (a) List the key steps involved in developing an actuarial model. (b) Explain why we need graduation. What do we actually test statistically? (c) What are the drawbacks of a y-- test? Explain how the sign test may overcome these. (d) Write a statistical hypothesis to test the adherence of the model to the data. (e) The life table data below provides an estimate d, of mortality rates obtained from a three-parameter Poisson model. Give the quality of goodness of-fit of the Poisson model by performing statistical tests based on:, and draw the conclusions. i. x-test. ii. Standardized deviations test. [Consider the following subintervals for the data range: A1 = (-00, -3], A2 = (-3, -2], As = (-2, -1], A4 = (-1, 0], As = (0, 1]. As = (1. 2], A7 = (2,3], and As = (3,co) .] iii. Sign test iv. Change-of-sign test v. Grouping-of-sign test vi. Lag-2 serial correlation test Age(x) d, 1 (x103) Z, 12 8119 14 2.3131 -1.09976140 17 7750 20 2.5394 0.07782846 22 6525 22 2.8858 0.73850019 27 5998 23 3.3961 0.59198689 32 5586 26 4.1353 0.61533059 37 5245 28 5.2145 0.13842351 42 4659 32 6.8040 0.07277321 47 4222 37 9.1829 -0.25757957 52 3660 44 12.8197 -0.38629208 3012 54 18.4927 -0.16160903 2500 68 27.5240 0.01527157 67 2113 87 42.1675 -0.02843635 1469 100 66.2083 0.62422085 77 883 95 105.7305 0.70883012 82 418 70 169.5455 0.62843083 87 181 49 267.4033 1.10547651 Table 3: Tabel of mortality rates