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A coffee vending machine is set to fill a cup with an average of 6.5 ounces...

A coffee vending machine is set to fill a cup with an average of 6.5 ounces of soft drink. The amount of fill varies. Sometimes the machine overfills the cup until it overflows and sometimes it fills it under the legal minimum. Suppose the amount of fill, X, follows the Normal distribution with an average of 6.5 ounces and a standard deviation of 0.3 ounces.

What is the probability that a 7-ounce cup overflows, that is, find P(X>7)?

A) Given the information above, what is the probability that a single fill is between 6 and 6.8 ounces, that is, find P(6<X<6.8).

B) Given the same information above, suppose a secretary needs to prepare 8 cups of coffee for a conference. What is the distribution of the average amount of the 8 cups of coffee, x¯?

C) Given the information above, what is the probability that the average amount of the 8 cups of coffee exceeds 6.7 ounces, that is, find P(x¯>6.7)P(x¯>6.7).

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