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

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

a. Calculate the value of f(x).

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

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

d. What is the probability that the next cup of coffee will contain exactly 7.5 ounces of coffee?

e. What is the probability that the next cup of coffee will contain less than 8.1 ounces of coffee?

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

g. What volume represents the 15th percentile of this distribution?

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