Soft-drink dispenser. The manager of a local soft-drink bottling company believes that when a new beveragedispensing machine is set to dispense 8 ounces, it in fact dispenses an amount x at random anywhere between 7.5 and 8.5 ounces, inclusive. Suppose x has a uniform probability distribution.

a. Is the amount dispensed by the beverage machine a discrete or a continuous random variable? Explain.

b. Graph the frequency function for x, the amount of beverage the manager believes is dispensed by the new machine when it is set to dispense 8 ounces.

c. Find the mean and standard deviation for the distribution graphed in part

b, and locate the mean and the interval m { 2s on the graph.

d. Find P1x Ú 82.

e. Find P1x 6 72

f. Find P17.75 6 x 6 8.252.
g. What is the probability that each of the next two bottles filled by the new machine will contain more than 8.25 ounces of beverage? Assume that the amount of beverage dispensed in one bottle is independent of the amount dispensed in another bottle.