Textbook Problem

Demand Using the probability density function in Exercise 38, determine the number of tons that should be ordered each week so that the demand can be met for 90% of the weeks.

Demand The weekly demand x (in tons) for a certain product is described by the probability density function

$f\left(x\right)=\frac{1}{36}x{e}^{-x/6},\left[0,\infty \right]$

Find and interpret each probability.

$\begin{array}{l}\left(\text{a}\right)P(x<6)\hfill \\ \left(\text{b}\right)P(6<x<12)\hfill \\ \left(\text{c}\right)P(12\le x\le 24)\hfill \\ \left(\text{d}\right)P(x>12)=1-P(x\le 12)\hfill \end{array}$