Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

1) A coffee dispensing machine fills cups to amounts that are uniformly distribu

ID: 3044678 • Letter: 1

Question

1) A coffee dispensing machine fills cups to amounts that are uniformly distributed. Specifically, if i select a small 12 oz coffee, the machine dispenses between 10 and 13 oz. of coffee, following a uniform distribution a) Is the amount of coffee dispensed by the machine a discrete or continuous randonm variable? Explain. b) Graph the probability function for P(x), where X is the amount of coffee dispensed when I select a small coffee c) Find the probability that my 12 oz. cup will not overflow, i.e. P(X s 12). d) How large of a coffee cup should i have if want to be 95% confident that the dispenser won't overfill the cup? (Hint: find P95).

Explanation / Answer

a) continuous , it can take any value from 10 to 13 oz
b)

probability is constant = 1/(13 -10) = 1/3

C)
P(X < 12) = (12 -10) /(13-10) = 2/3
d)
P(X < x)= 0.95
(x- -10) /(13-10) = 0.95
x = 10 + 3 * 0.95
= 12.85