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The attention span of teenagers at a large high school has an average length of $48\text{ minutes}$ with a standard deviation of $6.8\text{ minutes}$. Because some students in this school pay attention for significantly less amount of time, the distribution is strongly skewed to the left. Random samples of $400\text{ students}$ are taken with the average length of attention span, $\overline { x }$, being recorded for each sample.

Which of the following best describes the sampling distribution of $\overline { x }$?

A

Approximately normal with mean $48\text{ minutes}$ and standard deviation $0.34\text{ minutes}$.

B

Approximately normal with mean $48\text{ minutes}$ and standard deviation $6.8\text{ minutes}$.

C

Strongly skewed to the left with mean $48\text{ minutes}$ and standard deviation $0.017\text{ minutes}$.

D

Strongly skewed to the left with mean $48\text{ minutes}$ and standard deviation $0.34\text{ minutes}$.

E

Strongly skewed to the left with mean $48\text{ minutes}$ and standard deviation $6.8\text{ minutes}$.

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