random sample

26. Six Pepperidge Farm bagels were weighed, yielding the following data (grams):
117.6 109.5 111.6 109.2 119.1 110.8
(Note: 4 ounces = 113.4 grams)
a. Assuming that the six bagels are a random sample and the weight is normally distributed, estimate the true average weight and standard deviation of the weight using maximum likelihood.
b. Again assuming a normal distribution, estimate the weight below which 95% of all bagels will have their weights. (Hint: What is the 95th per- centile in terms of m and s? Now use the invari- ance principle.)