Up until the early 1900s, people who colored their hair used only herbs and natural dyes. Today, hair-coloring products contain two main ingredients: hydrogen peroxide and ammonia. The makers of a Clairol hair-color product claim the mean amount of hydrogen peroxide in each bottle is 0.10 mg/m3 . Assume the standard deviation is 0.05 mg/m3 . A random sample of these hair-color products was obtained, and the amount of hydrogen peroxide in each bottle was measured. The resulting data (in mg/m") are given in the table below. 0.14 0.15 0.19 0.13 0.14 0.06 0.16 0.09 0.11
0.13 0.16 0.23 0.09 0.13 0.09 0.09 0.12 0.06
0.14 0.22 0.13 0.10 0.02 0.12 0.06 0.10 0.13
0.18 0.12 0.21

Required:
a. Suppose the manufacturer's claim is true. Find the distribution of the sample mean.
b. Is there any evidence to suggest the manufacturer is including too much hydrogen peroxide in the product?