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{(1)/(7)}`

Explanation:

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

`f(x)=(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)=(1)/(20-13)=(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)((1)/(7))\ dx\\\\= (1)/(7)[x]^(20)_(19)\\\\=(1)/(7)[20-19]=(1)/(7)`

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