Most of the answer to this use a formula similar to EX = xf(x)dx, but I don't understand why it gets divided by 2?

4. [Coffee Machine] [30 points] Consider the amount of coffee in ounces that will be dispensed in a cup when a certain automatic coffee dispensing machine is activated. Suppose that the machine never dispenses less than 6 or more than 8 ounces. Within this range, any quantity is as likely to be dispensed as any other, i.e., the amount of coffee dispensed is a continuous random variable, with the probability density function being a constant within the range. (5pts) What is the probability that the amount of coffee dispensed in a cup is less than 7.6 ounces? (5pts) Suppose the coffee machine was activated for 10 times. What is the probability that the amount of coffee will be more than 7.6 ounces in at most 1 of the 10 cups? Keep the second decimal place in your answer . (c) (10pts) It can be shown that the expected amount of coffee dispensed in a cup is equal to 7 ounces, and SD is . Suppose the coffee machine was activated for 100 times. What is the mean and SD for the total amount of coffee in ounces dispensed? (d) (10pts) Suppose the coffee machine was activated for 100 times. Use normal approximation with continuity correction to find the probability that between 15 and 25 (inclusive) cups will have more than 7.6 ounces of coffee. Be sure to verify the condition of normal approximation first. Keep the 4th decimal place in your final