Deer mice (Peromyscusmaniculatus) are small rodents native to North America. Their body lengths excluding tails is known to vary approximately Normally with mean µ = 86 mm and standard deviation σ = 8 mm. Deer mice are found in diverse habitats and exhibit different adaptations to their environment. A random sample of 14 deer mice in a rich forest habitat gives an average body length of `x= 91.1 mm. Assume that the standard deviation σ of all deer mice in this area is 8 mm. Show any work.

a. What is the standard deviation of the mean length `x?

b. What critical value do you need toin order to compute a 95% confidence interval for the meanµ?

c. Calculate a 95% confidence interval for the mean body length of all deer mice in the forest habitat.

d. State explicitly what this confidence level means.