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

question 67

Multiple Choice

Identify the distribution of the sample mean. In particular, state whether the distribution of $\bar { x }$ is normal or approximately normal and give its mean and standard deviation.
-For the population of one town, the number of siblings, $x$ , is a random variable whose relative frequency histogram has a reverse J-shape. The mean number of siblings is $1.1$ and the standard deviation is 1.3. Let $\bar { x }$ denote the mean number of siblings for a random sample of size 39 .
Determine the sampling distribution of the mean for samples of size 39 .

• A)Normal, mean \(= 1.1\), standard deviation \(= 1.3\)
• B) Approximately normal, mean \(= 1.1\), standard deviation \(= 0.21\)
• C) Normal, mean \(= 1.1\), standard deviation \(= 0.21\)
• D) Approximately normal, mean \(= 1.1\), standard deviation \(= 1.3\)

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Definitions:

Cellulitis

An infection of the skin and tissues beneath the skin, often characterized by redness, pain, and swelling.

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Located or applied under the skin, often referring to the layer of fat and tissue beneath the skin's surface.

Ingestion

The act of taking food, drinks, or other substances into the body through the mouth.

Absorption

The process by which substances are taken up into the bloodstream, particularly in the context of nutrients from the digestive system.