5 A new dairy product is tested extensively to determine its shelf life in days. The measure- ments can be modelled by the following probability density function. St/72 S(t) = 0st< 12 otherwise. Let T denote the amount of time (in days) it takes for an instance of this new dairy product to expire. (a) Sketch a graph of f(t). (b) Find the cumulative distribution function F(t) for T. (c) What is the probability the dairy product will not expire in the first 7 days? (d) What is the probability the dairy product expires after five days but before the end of the tenth day? (e) If the dairy product doesn't expire in the first five days, what is the probability it will last at least ten days before expiring?

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