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Math·Problem-Solving and Data Analysis·Inference from sample statistics and margin of error

hard

An inspector checked a sample of $330$ scales selected at random from a population of $8,000$ scales to estimate what percentage of the $8,000$ scales were inaccurate. From this sample, the inspector estimated that $7\%$ of the $8,000$ scales were inaccurate, with an associated margin of error of $2.8\%$. Which of the following is the most appropriate conclusion?

A

It is plausible that between $336$ and $784$ of the scales in the population are inaccurate.

B

It is plausible that fewer than $336$ of the scales in the population are inaccurate.

C

Exactly $560$ of the scales in the population are inaccurate.

D

It is plausible that more than $784$ of the scales in the population are inaccurate.