Following are the ages of the Grammy award winners for Best New Artist for the years 2013–2017.

(For Fun., the age is that of guitarist Andrew Dost. For Macklemore & Ryan Lewis the age is that of Benjamin Haggerty (Macklemore). Ages are given to the nearest half year so the five ages are all different.)

a. Consider this to be a population. Find the population mean ????
and the population standard deviation σ.

b. List all samples of size 2 drawn with replacement. There are 5 × 5 = 25 different samples.

c. Compute the sample mean x̄ for each of the 25 samples of size 2.

Compute the mean μ x̄ and the standard deviation σx̄ of the sample means.

d. Verify that μ x̄ = μ and σ x̄ = σ∕√2.

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Year: Winner Age 2017: Chance the Rapper 23.5 2015: Sam Smith 2016: Meghan Trainor 2014: Macklemore & Ryan Lewis 30.5 22 22.5 2013: Fun. 29.5