After reviewing historical data in the form of a relative frequency histogram, the quality control manager at the Eagle Winery in Napa Valley, California believes that number of milliliters (ml) injected into the winery's standard size wine bottles (containing non-vintage red table wine) is normally distributed with mean 750 ml and standard deviation 4.5 ml.

a. Find the probability that a randomly selected standard size wine bottle that has been filled with wine will contain between 743 ml and 746 ml.

b. Find the probability that a randomly selected standard size wine bottle that has been filled with wine will contain between 748 ml and 752 ml.

c. Find the probability that a randomly selected standard size wine bottle that has been filled with wine will contain more than 759 ml.

d. Find the value of x0 that makes the following statement true: 7.5% of standard size wine bottles filled by the Eagle Winery contain more than x0 milliliters.

e. Suppose that 50 filled standard size wine bottles are randomly selected and the number of milliliters of wine injected into a bottle follows the normal distribution specified by the quality control manager. What is the probability that the mean number of milliliters injected into these 50 bottles is more than 751.75 ml? List any assumptions that you make.