An imaginative anthropzlogist measured the stature of 100 hobbits (using the proper English measure of inches) and found these values: ∑X = 3600 ∑X2 = 130,000 Assume that the heights of hobbits are...

An imaginative anthropzlogist measured the stature of 100 hobbits (using the proper English measure of inches) and found these values:

Assume that the heights of hobbits are normally distributed. Find μ and σ and answer the following questions.

a. The Bilbo Baggins Award for Adventure is 32 inches tall. What proportion of the hobbit population is taller than the award?

b. Three hundred hobbits entered a cave that had an entrance 39 inches high. The orcs chased them out. How many hobbits could exit without ducking?

c. Gandalf is 46 inches tall. What is the probability that he is a hobbit?