Identify the Distribution of the Sample Mean $\bar { x }$

question 30

Multiple Choice

Identify the distribution of the sample mean. In particular, state whether the distribution of $\bar { x }$ is normal or approximatelynormal and give its mean and standard deviation.
-Let $x$ represent the number that shows up when a balanced die is rolled. Then $\mathrm { x }$ is a random variable with a mean of $3.5$ and a standard deviation of 1.71. Let $\bar { x }$ denote the mean of the numbers obtained when the die is rolled 40 times. Determine the sampling distribution of $\bar { x }$ .

• A)Normal, mean \(= 3.5\), standard deviation \(= 0.04\)
• B) Normal, mean \(= 3.5\), standard deviation \(= 0.27\)
• C) Approximately normal, mean \(= 3.5\), standard deviation \(= 0.27\)
• D) Approximately normal, mean \(= 3.5\), standard deviation \(= 1.71\)

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