You are an engineer at Leuranink developing computer chips to implant into people's brains. You have just completed the latest round of animal testing, the results of which are in the table to the right. Your boss, Melon Usk, has asked you to analyze the records to see if you can model the survival (or reliability) of the rodent patients who received Leuranink implants. Unfortunately, Usk's dog ate some of the rats prematurely, but at least you were able to catalog them! The table to the right provides the cage number, age of the rate (in months), the \"Eaten date\" (the number of days post-implant when the rat was eaten by Usk's dog). and \"Death date\" (the number of days post-implant the rat died \"naturally). a. [10 points] Using the Kaplan-Meier method, find the empirical model for the natural survival of rodents receiving the implant. b. [10 points] We also want to understand whether the Cage | Age | Eaten | Death # | (mo) | date date 1 7 60 1 2 19 1 29 52 1 35 15 1 12 3 2 28 13 2 15 23 2 22 34 2 30 28 2 19 7 3 20 11 3 13 70 3 14 16 3 8 4 3 16 40 survival rate 1s related to time spent in recovery following the implantation. Plot the data as 1f 1t were a Weibull distribution. Use the plot to estimate the parameters of the Weibull distribution that represent the fatality rate per day after implant. c. [5 points] We want to determine whether the age of the rat 1s influencing the survival rate. Using only the data for the rats that died naturally, determine whether there 1is a correlation in your sample and explain what it means