Suppose the times required for a cable company to fix cable problems in its customers' homes are uniformly distributed between 10 minutes and 25 minutes. What is the probability that a randomly selected cable repair visit will take at least 15 minutes?
Solution
Let $X$ denote the times required for a cable company to fix cable problems in its customers' home.
Given that $X\sim U(10,25)$. The pdf of $X$ is
$$ \begin{aligned} f(x) &= \frac{1}{25-10},10\leq x\leq 25\\ &=\frac{1}{15},10\leq x\leq 25 \end{aligned} $$
The probability that a randomly selected cable repair visit will take at least 15 minutes is
$$ \begin{aligned} P(X\geq 15) &= \int_{15}^{25} f(x) \; dx\\ &= \frac{1}{15}\int_{15}^{25} \; dx\\ &= \frac{1}{15}\big[x\big]_{15}^{25} \\ &= \frac{1}{15}\big[ 25-15]\\ &= 0.6667 \end{aligned} $$
Further Reading
- Statistics
- Descriptive Statistics
- Probability Theory
- Probability Distribution
- Hypothesis Testing
- Confidence interval
- Sample size determination
- Non-parametric Tests
- Correlation Regression
- Statistics Calculators
