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...

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.

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? Justify your answer.

A floor slip tester is used to measure the safety of a floor by comparing the measured coefficient of static friction with accepted standards and guidelines. Several factors can affect floor safety, for example, dampness, polishes, and maintenance chemicals. A marble floor is consider safe if the coefficient of static friction is no greater than 0.5. A random sample of 50 rainy days was selected, and the coefficient of static friction for the marble floor was measured on each day. The resulting sample mean was 0.6. Is there any evidence to suggest the marble floor is unsafe on rainy days? Assume the underlying population standard deviation is 0.2 and justify your answer.