A consumer research organization was interested in determining the mean number of credit cards owned by adults living in Kansas. To investigate, surveys were mailed to a random sample of $500$ adults with a Kansas address. However, only $84$ adults actually answered and returned the survey.

Given the following facts:

The population parameter is known to be $2.8$ credit cards.

The sample mean was found to be $2.9$ credit cards.

The standard deviation, $\sigma$ is $0.7$ credit cards.

Describe the sampling distribution of $\bar{x}$.

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