2. The manager of a local soft drink bottling Company believes that when a new beverage- dispensing machine is set to dispense 7 ounces, it infact dispenses an amount x at random anywhere between 6.5 and 7.5 ounces inclusive. Suppose x has a uniform probability distribution.

Required:

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 7 ounces.

c. Find the mean and standard deviation for the distribution graphed in part b, and locate the mean and the interval 2 on the graph

d. Find p(x 7)

e. Find P(6.5 x 7.25)