The manager of a local soft-drink bottling company believes that when a new beverage-dispensing machine is set to dispense 7 ounces, it in fact] dispenses an amount x at random anywhere between 65 and 7.5 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 7 ounces.
c. Find the mean and standard deviation for the distribution graphed in part b and locate the mean and the interval μ ± 2σ on the graph.
d. Find P(x ≥ 7).
e. Find P(x < 6).
f. Find P(6.5 ≤ x ≤ 7.25).
g. What is the probability that each of the next six bottles filled by the new machine will contain more than 725 ounces of beverage? Assume that the amount of beverage dispensed in one bottle is independent of the amount dispensed in another bottle.