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Probability Distribution of Hummingbirds Eggs Incubation Time

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10. Wildlife Hummingbirds Selasphorus sasin is the scientific name for what is commonly called "Allen Hummingbird" This beautiful hummingbird lives on the west coast of the United States and is named C.A. Allen (1841-1930) , who studied these birds extensively. Let x be a random variable that represents the incubation time for the Allen Hummingbird eggs. The x distribution has a mean of µ = 16 days. Let us assume that the standard deviation is approximately σ = 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 xbar be the average incubation time for these eggs.

a) What can we say about the probability distribution of xbar? It is approximately normal? What are the mean and standard deviation?
b) What is the probability of xbar is between 16 and 17 days?
c) What is the probability that xbar is less than 15 days?

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