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:

Egocentrism

The inability to distinguish between one's own perspective and someone else's perspective.

Artificialism

In the context of developmental psychology, it is the belief common in children that the environment and its features are created by human beings.

Symbolic

Pertains to the use of symbols, signs, or objects to represent ideas or concepts, a fundamental aspect of human communication and thought.

Dreams

A series of thoughts, images, and sensations occurring in a person's mind during sleep.