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 of ? = 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 842 and 864 grams. (Give your answer correct to four decimal places.)
(c) Describe the distribution of x, the mean weight for a sample of 30 such jars of sauce.
(d) Find the mean of the x distribution. (Give your answer correct to the nearest whole number.)
(ii) Find the standard error of the x distribution. (Give your answer correct to two decimal places.)
(e) Find the probability that a random sample of 30 jars has a mean weight between 842 and 864 grams. (Give your answer correct to four decimal places.)