Question: Let p(t) = 0.0375t 2 + 0.225t be the density function for the shelf life of a brand of banana, with t in weeks and

Let p(t) = −0.0375t² + 0.225t be the density function for the shelf life of a brand of banana, with t in weeks and 0 ≤ t ≤ 4. See Figure 7.19.

$fraction of bananas per week of age 0.4 0.3 0.2 0.1 1$

(a) Sketch the cumulative distribution function for the shelf life of bananas.
(b) Use the cumulative distribution function to estimate the probability that a banana lasts between 1 and 2 weeks. Check with Problem 16(a).

fraction of bananas per week of age 0.4 0.3 0.2 0.1 1 p(t) = -0.03751 +0.225t 2 3 Figure 7.19 4 t (weeks)

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