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The choice of an appropriate statistical model for a real‐life application is often difficult. Standard examples given in a traditional calculus‐based course in probability and statistics do not provide students with a taste of the challenge usually associated with finding a satisfactory theoretical probability distribution in certain important applications. In addition, the assessment of the goodness of fit in practical terms is not usually discussed. To illustrate the difficulties of modelling, analytical laws of mortality are proposed using probability functions that are commonly discussed in a standard probability and statistics text intended for undergraduates in mathematics and statistics. An assessment is made of the resulting quality of approximations obtained for the valuation of premiums regarding a term life insurance policy.
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