Question 1192631: Suppose the times required for a cable company to fix cable problems in its customers’ home are uniformly distributed between 10 minutes and 25 minutes.
a.What is the probability that a randomly selected cable repair visit will take at least 15 minutes?
b.What is the probability that a cable repair visit will take over 20 minutes given that it takes over 15 minutes?
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! **a. Probability of a visit taking at least 15 minutes**
* **Uniform Distribution:** In a uniform distribution, the probability density function is constant within the given interval.
* **Calculate the total interval:**
* Total interval = 25 minutes - 10 minutes = 15 minutes
* **Calculate the probability density:**
* Probability density (f(x)) = 1 / (total interval) = 1 / 15
* **Calculate the probability of a visit taking at least 15 minutes:**
* This is the probability of the visit taking between 15 minutes and 25 minutes.
* Length of this interval: 25 minutes - 15 minutes = 10 minutes
* Probability = (length of interval) * (probability density) = 10 minutes * (1/15) = 2/3
**Therefore, the probability that a randomly selected cable repair visit will take at least 15 minutes is 2/3 or approximately 0.667.**
**b. Probability of a visit taking over 20 minutes given it takes over 15 minutes**
* **Conditional Probability:** We are given that the visit takes over 15 minutes. This becomes our new "total interval."
* **New total interval:** 25 minutes - 15 minutes = 10 minutes
* **Length of the interval where the visit takes over 20 minutes:** 25 minutes - 20 minutes = 5 minutes
* **Probability:** 5 minutes / 10 minutes = 1/2
**Therefore, the probability that a cable repair visit will take over 20 minutes given that it takes over 15 minutes is 1/2 or 0.5.**
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