The amount of fill (weight of contents) put into a glass jar of spaghetti sauce is normally distributed with mean   850 grams and standard deviation   8 grams.

a. Describe the distribution of x, the amount of fill per jar.

b. Find the probability that one jar selected at random contains between 848 and 855 grams.

c. Describe the distribution of x, the mean weight for a sample of 24 such jars of sauce.

d. Find the probability that a random sample of 24 jars has a mean weight between 848 and 855 grams.