Answer:
0.8333 = 83.33% probability that the cycle time exceeds 50 minutes if it is known that the cycle time exceeds 45 minutes
Step-by-step explanation:
A distribution is called uniform if each outcome has the same probability of happening.
The uniform distributon has two bounds, a and b, and the probability of finding a value higher than x is given by:
![P(X > x) = \frac{b - x}{b - a}](https://tex.z-dn.net/?f=P%28X%20%3E%20x%29%20%3D%20%5Cfrac%7Bb%20-%20x%7D%7Bb%20-%20a%7D)
Uniformly distributed over the interval 40 to 75 minutes.
This means that ![a = 40, b = 75](https://tex.z-dn.net/?f=a%20%3D%2040%2C%20b%20%3D%2075)
It is known that the cycle time exceeds 45 minutes
This means that we can use ![a = 45](https://tex.z-dn.net/?f=a%20%3D%2045)
What is the probability that the cycle time exceeds 50 minutes?
![P(X > 50) = \frac{75 - 50}{75 - 45} = 0.8333](https://tex.z-dn.net/?f=P%28X%20%3E%2050%29%20%3D%20%5Cfrac%7B75%20-%2050%7D%7B75%20-%2045%7D%20%3D%200.8333)
0.8333 = 83.33% probability that the cycle time exceeds 50 minutes if it is known that the cycle time exceeds 45 minutes