One dimension of bird beaks is “depth”—the height of the beak where it arises from the bird’s head. During a research study on one island in the Galapagos archipelago, the beak depth of all Medium Ground Finches on the island was found to be Normally distributed with mean μ = 9.5 millimeters (mm) and standard deviation σ = 1.0 mm.9

a. Choose an SRS of 5 Medium Ground Finches from this population. Describe the sampling distribution of x¯.

b. Find the probability that x¯ estimates μ within ±0.5 mm. (This is the probability that x¯ takes a value between 9 and 10 mm.)

c. Choose an SRS of 50 Medium Ground Finches from this population. Now what is the probability that x¯ falls within ±0.5 mm of μ? In what sense is the larger sample “better”?