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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 $\bar{x}$.

A

Since a few people probably have a lot of credit cards, the sampling distribution would be skewed right with a center at $2.8$ and a standard deviation of $0.076$.

B

Since a few people probably don't have any credit cards at all, the sampling distribution would be skewed left with a center at $2.9$ and a standard deviation of $0.7$.

C

Since the sample size of $500$ is sufficiently large, the sampling distribution will be approximately normal with a center at $2.9$ and a standard deviation of $22.36$.

D

Since the sample size of $84$ is sufficiently large, the sampling distribution will be approximately normal with a center at $2.8$ and a standard deviation of $0.076$.

E

Since the sample size of $84$ is sufficiently large, the sampling distribution will be approximately normal with a center at $2.8$ and a standard deviation of $0.7$.

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