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 pdf $f(x)$ is

The probability that store charge more than \$ 2.7 per gallon is

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

Thus $10$ percent of stores that charge more than $2.70 per gallon.

#### Further Reading

- Statistics
- Descriptive Statistics
- Probability Theory
- Probability Distribution
- Hypothesis Testing
- Confidence interval
- Sample size determination
- Non-parametric Tests
- Correlation Regression
- Statistics Calculators