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Random Variables and Distributions
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Sampling distribution of the sample mean: Mean and standard deviation
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During a wisdom teeth removal procedure, \( 1,2,3 \), or 4 wisdom teeth are removed, depending on the patient's needs. Records indicate that nationwide, the mean number of wisdom teeth removed in a procedure is \( \mu=3.86 \), with a standard deviation of \( \sigma=0.99 \). Suppose that we will take a random sample of 7 wisdom teeth removal procedures and record the number of wisdom teeth removed in each procedure. Let \( \bar{x} \) represent the sample mean of the 7 procedures. Consider the sampling distribution of the sample mean \( \bar{x} \).
Complete the following. Do not round any intermediate computations. Write your answers with two decimal places, rounding if needed.
(a) Find \( \mu- \) (the mean of the sampling distribution of the sample mean).
\[
\mu_{-}=\square
\]
(b) Find \( \sigma \frac{-}{x} \) (the standard deviation of the sampling distribution of the sample mean).
\[
\sigma_{-}=\square
\]
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