The stirrup bone, located in the middle ear, is the smallest bone in the human body, with a mean length of 3 mm.30 Suppose the standard deviation of the length is 0.16 mm. This bone, located in the ear, is part of a leverage system that can affect hearing. There is some speculation that high noise levels can affect the development of this bone and inhibit hearing. In a random sample of adults who have lived in a large city their entire lives, the length of the right-ear stirrup bone was obtained for each.
a. Find the distribution of the sample mean. Carefully sketch the probability density function.
b. Is there any evidence to suggest the length of the stirrup bone for lifetime city adults is different from 3 mm? Justify your answer.