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 percentile in terms of μ and σ? Now use the invariance principle.)