Question

chapter 6 quiz - continuous probability distributions
10 points possible answered: 5/11
question 8
bus wait times are uniformly distributed between 11 minutes and 29 minutes. the unshaded rectangle below with area 1 depicts this. the shaded rectangle depicts the probability that a randomly selected bus wait time will be between 18 and 24 minutes.
find the probability that a person waits between 18 and 24? (round answer to at least 4 decimal places)

Explanation:

Step1: Identify the formula for uniform - distribution probability

The probability density function for a uniform distribution on the interval $[a,b]$ is $f(x)=\frac{1}{b - a}$, and the probability $P(c\leq X\leq d)=\frac{d - c}{b - a}$, where $a$ is the lower - bound of the distribution, $b$ is the upper - bound, $c$ is the lower - bound of the sub - interval, and $d$ is the upper - bound of the sub - interval. Here, $a = 11$, $b = 29$, $c = 18$, and $d = 24$.

Step2: Calculate the probability

$P(18\leq X\leq 24)=\frac{24 - 18}{29 - 11}=\frac{6}{18}=\frac{1}{3}\approx0.3333$.

Answer:

$0.3333$