Question

The amount of time it takes Isabella to wait for the bus is continuous and uniformly distributed between 3 minutes and 17 minutes. What is the probability that it takes Isabella more than 5 minutes to wait for the bus

Answer 1

Answer:

P(X>5) = 0.857

Step-by-step explanation:

Let X $\sim$ uniform(3.17)

$f(x) = \dfrac{1}{17-3} ; \ \ \ 3 \le x \le 17$

The required probability that it will take Isabella more than 5 minutes to wait for the bus can be computed as:

$P(X > 5) = \int ^{17}_{5} f(x) \ dx$

$P(X > 5) = \int ^{17}_{5} \dfrac{1}{17-3} \ dx$

$P(X > 5) =\dfrac{1}{14} \Big [x \Big ] ^{17}_{5}$

$P(X > 5) =\dfrac{1}{14} [17-5]$

$P(X > 5) =\dfrac{12}{14}$

P(X>5) = 0.857