Question: Selasphorus sasin is the scientific name for what is commonly called “Allen’s hummingbird.” This is beautiful hummingbird lives on the West Coast of the United States and is named for C.A. Allen (1841-1930), 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 (Little, Brown and Company), the x distribution has a mean of \[\mu \] = 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 an incubator. Let \[\bar{X}\] be the average incubation time for these eggs.

a.) What can we say bout the probability distribution of \[\bar{X}\] ? 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 than 15 days?