Question

suppose that the waiting times at an emergency room of a miami hospital are uniformly distributed between 0 minutes and 50 minutes. the worst 25% waiting times are

inse
a. greater than or equal to 37.5 minutes
b. greater than or equal to 25 minutes
c. less than or equal to 12.5 minutes
d. less than or equal to 20 minutes

Explanation:

Step1: Recall uniform - distribution formula

For a uniform distribution $U(a,b)$ (here $a = 0$, $b = 50$), the cumulative - distribution function is $F(x)=\frac{x - a}{b - a}$ for $a\leq x\leq b$.

Step2: Find the value corresponding to the 75th percentile

We want to find the value $x$ such that $P(X\leq x)=0.75$. Using the CDF formula $F(x)=\frac{x - 0}{50-0}=\frac{x}{50}$.
Set $\frac{x}{50}=0.75$.

Step3: Solve for $x$

Multiply both sides of the equation $\frac{x}{50}=0.75$ by 50. We get $x = 0.75\times50=37.5$. The worst 25% of waiting times are the times greater than or equal to the 75th percentile.

Answer:

A. greater than or equal to 37.5 minutes