Question Tag: insurance policies

An Actuary in an insurance company formulates insurance policies that will be both profitable and marketable. For a particular policy, the lifetimes of the policyholders follow a normal distribution with a mean of 66.20 years and standard deviation of 4.4 years. One of the options with this policy is to receive a payment following the $65^{\mathrm{h}$ birthday and a payment every five years thereafter. Let $X$ be the age at death (in years) of a policyholder                                                                                                        (a) Draw the graph of the distribution of $X$ showing clearly the key decision numbers i.e. 66.2 years, 4.4years, 65years, 70years, 75years.                                                                                                                                                                                                              (b) Determine the                                                                                                                                                                                                          (i) percentage of policyholders who will receive at least one payment using the option above.                                                                    (ii) percentage of policyholders who will receive two or more payments.                                                                                                          (iii) percentage of policyholders who will receive exactly two payments.