Calculate normal proportions, sketch an interval and determine a warranty quantile.

A company manufactures television sets. They claim that the lifetime of a set is normally distributed with a mean of 80 months and standard deviation of 8 months.

1. What proportion of television sets break down in less than 72 months?[2]
2. [5]
   1. Calculate the proportion of sets which have a lifetime between 72 months and 90 months.
   2. Illustrate this proportion by appropriate shading in a sketch of a normal distribution curve.
3. If a set breaks down in less than x months, the company replace it free of charge. They replace 4% of the sets. Find the value of x.[3]