Standard Deviation Given Only the Mean

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A company that manufactures large LCD screens knows that not all pixels on their screen​ light, even if they spend great care when making them. In a sheet 6 ft by 12 ft that will be cut into smaller​ screens, they find an average of 5.7 blank pixels. They believe that the occurrences of blank pixels are independent.

What is the Standard Deviation of blank pixels / square foot?

I can't figure out how to calculate SD when only given the mean. the mean is 0.079 blank pixels per square foot

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Without any other information, it is not possible to deduce the Standard deviation from the mean alone. Presumably someone at the company has access to the data used to calculate the mean. That very same dataset should help you calculate all the stats that you need.