Question: Selasphorus sasin in the scientific name for what is commonly called "Allen's hummingbird." This beautiful hummingbird lives on the West Coast of the U.S. and is named for C.A. Allen, who studied these birds extensively. Let x be a random variable that represents the incubation time for Allen hummingbird eggs. Based on information from The Hummingbird Book, by Donald and Lillian Stokes, the x distribution has a mean of μ = 16 days. Let us assume that the standard deviation is approximately ? = 2 days. The distribution of x values is more or less mound shaped and symmetrical but not necessarily normal. Suppose that we have n = 30 eggs in the incubator. Let x be the average incubation time for these eggs.

(a) What can we say about the probability distribution of x? Is it approximately normal? What are the mean and standard deviation?

(b) What is the probability that \(\bar{X}\) is between 16 and 17 days?

(c) What is the probability that \(\bar{X}\) is less that 15 days?