Actuarial Science (stats) question, please show all work

As part of a mortality study, ten newborns were observed until each either died or withdrew from the study. The table below shows the age at death or withdrawal of each individual. Individual Age at Death Age at Withdrawal 12 35 55 59 61 66 73 73 80 90 (a) Show that the Kaplan-Meier estimate of S(80) is 0.2 to the nearest 0.1. You should calculate the value to the nearest 0.001. (b) (i) Construct an approximate 95% linear confidence interval for the Kaplan-Meier estimate of S(80), using a normal approximation and Greenwood's approximation to the variance of this estimator. (ii) Construct an approximate 95% log-transformed confidence interval for the Kaplan- Meier estimate of S(80). (iii) Explain briefly why the log-transformed interval is a better estimate in this case