The diameters of fully grown white oak trees are normally distributed, with a mean of 3.5 feet

Question:

The diameters of fully grown white oak trees are normally distributed, with a mean of 3.5 feet and a standard deviation of 0.2 foot, as shown in the figure. Random samples of size 16 are drawn from this population, and the mean of each sample is determined. Find the mean and standard deviation of the sampling distribution of sample means. Then sketch a graph of the sampling distribution.

Distribution of Population Diameters

a. Find μ_x̅ and σ_x̅.

b. Sketch a normal curve with mean μ_x̅ and standard deviation σ_x̅.

Distribution
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