Question

The amount of time it takes Victoria to solve crossword puzzles can be modeled by a continuous and uniformly distributed random time between 4 minutes and 12 minutes. What is the probability that it will take Victoria greater than 8 minutes (total) for a puzzle that she has already been working on for 7 minutes?

Answer 1

80% probability that it will take Victoria greater than 8 minutes (total) for a puzzle that she has already been working on for 7 minutes

Explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X greater than x is given by the following formula.

`P(X > x) = 1 - (x - a)/(b-a)`

Uniformly distributed random time between 4 minutes and 12 minutes.

This means that
`a = 4, b = 12`

What is the probability that it will take Victoria greater than 8 minutes (total) for a puzzle that she has already been working on for 7 minutes?

Already working for 7 minutes, so a is updated to 7.

`P(X > 8) = 1 - (8 - 7)/(12 - 7) = 0.8`

80% probability that it will take Victoria greater than 8 minutes (total) for a puzzle that she has already been working on for 7 minutes