Question

Suppose the times required for a cable company to fix cable problems in its customers' homes are uniformly distributed between 13 minutes and 20 minutes. What is the probability that a randomly selected cable repair visit will take at least 19 minutes? (Enter the final answers reduced to the lowest possible fraction.)

Answer 1

Answer:  $\mathbf{\dfrac{1}{7}}$

Step-by-step explanation:

The probability density function for x which is uniformally distributed in interval [a,b] is given by :-

$f(x)=\dfrac{1}{b-a}$

Given : The times required for a cable company to fix cable problems in its customers' homes are uniformly distributed between 13 minutes and 20 minutes.

Then, $f(x)=\dfrac{1}{20-13}=\dfrac{1}{7}$

Now, the probability that a randomly selected cable repair visit will take at least 19 minutes will be :_

$\int^{20}_{19}\ f(x)\ dx\\\\=\int^{20}_{19}(\dfrac{1}{7})\ dx\\\\= \dfrac{1}{7}[x]^{20}_{19}\\\\=\dfrac{1}{7}[20-19]=\dfrac{1}{7}$

Hence, the probability that a randomly selected cable repair visit will take at least 19 minutes = $\mathbf{\dfrac{1}{7}}$