Question

A vending machine located in a local office dispenses coffee that varies from 7.4 to 8.2 ounces. The volume of the coffee dispensed follows a continuous uniform distribution

a. What is the probability that the next cup of coffee will contain more than 8.0 ounces of coffee?

b. What is the probability that the next cup of coffee will contain less than 7.8 ounces of coffee?

c. What is the probability that the next cup of coffee will contain between 7.5 and 8.0 ounces of coffee?

d. What are the mean and standard deviation for this distribution?

Answer 1

Uniform distribution: a = 7.4 ounces, b = 8.2 ounces

a) P(next cup of coffee will contain more than 8.0 ounces of coffee) = P(X > 8)

= (8.2 - 8)/(8.2 - 7.4)

= 0.2/0.8

= 0.25

b) P(next cup of coffee will contain less than 7.8 ounces of coffee) = P(X < 7.8)

= (7.8 - 7.4)/0.8

= 0.5

c) P(next cup of coffee will contain between 7.5 and 8.0 ounces of coffee) = P(7.5 < X < 8.0)

= (8.0 - 7.5)/0.8

= 0.625

d) Mean = (a + b)/2

= (7.4 + 8.2)/2

= 7.8

Standard deviation =

=

= 0.231