Suppose Coke bottles have volumes that are normally distributed with a mean of 298ml and a standard deviation of 3ml. An

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Suppose Coke bottles have volumes that are normally distributed
with a mean of 298ml and a standard deviation of 3ml. Answer the
following questions and show your work.
(i) We take a random sample of 9 bottles and calculate the
average volume. What is the probability
the average volume is less than
295ml?
(ii) What volume is the cutoff for the top 1% of
the average volume of a random
sample of 9 bottles?
(iii) If the shape of the distribution of the volumes is not
normal (the mean and the standard deviation remain the same), would
your calculation in the previous questions still be
valid? Explain.