Answer:
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
Step-by-step 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 - \frac{x - a}{b-a}](https://tex.z-dn.net/?f=P%28X%20%3E%20x%29%20%3D%201%20-%20%5Cfrac%7Bx%20-%20a%7D%7Bb-a%7D)
Uniformly distributed random time between 4 minutes and 12 minutes.
This means that ![a = 4, b = 12](https://tex.z-dn.net/?f=a%20%3D%204%2C%20b%20%3D%2012)
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 - \frac{8 - 7}{12 - 7} = 0.8](https://tex.z-dn.net/?f=P%28X%20%3E%208%29%20%3D%201%20-%20%5Cfrac%7B8%20-%207%7D%7B12%20-%207%7D%20%3D%200.8)
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