Question

Question 2     

A coffee dispenser machine fills cups at amounts that are uniformly distributed. Specifically, the machine dispenses between 10oz and 13oz of coffee, following a Uniform distribution. I select a small 12oz cup.

1. Is the amount of coffee dispensed a discrete or continuous random variable? Explain.
2. Graph the probability function for P(X), where X is the amount of coffee dispensed.
3. What is the average amount of coffee dispensed?
4. What is the more likely amount (mode) of coffee that will be dispensed?
5. What is P( X = 12) ?
6. Find the probability that my 12oz. cup will not overflow, i.e. P( X ≤ 12).
7. How large of a coffee cup should I have if I want to be 95% confident that the dispenser won't overfill the cup?

Answer 1