# Solved:The price for a gallon of whole milk is uniformly distributed between

Sep 20, 2020

The price for a gallon of whole milk is uniformly distributed between \$2.25 and \$2.75 during July in the U.S. Give the equation and graph the pdf for X, the price per gallon of whole milk during July. Also determine the percent of stores that charge more than \2.70 per gallon. #### Solution The probability density curve is  \begin{aligned} f(x)=\left\{ \begin{array}{ll} \frac{1}{2.75 - 2.25}=2 , & \hbox{2.25 \leq x\leq 2.75;} \\ 0, & \hbox{Otherwise.} \end{array} \right. \end{aligned}  a. The graph of the pdff(x)$is The probability that store charge more than \$ 2.7 per gallon is

 \begin{aligned} P(X\geq 2.7) &= \int_{2.7}^{2.75} f(x) \; dx\\ &= \frac{1}{2.75-2.25}\int_{2.7}^{2.75} \; dx\\ &= 2\big[x\big]_{2.7}^{2.75} \\ &= 2\big[ 2.75- 2.7]\\ &= 0.1 \end{aligned}