In terms of the percentage of downloaded books, the sampling distribution's mean is 0.03 and its standard deviation is 0.0197.
Central Limit Theorem:
The sampling distribution of the sample percentage for a proportion p in a sample of size n will be roughly normal with a mean (μ = p) and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n} }[/tex].
In a given year, 3% of books checked out from the library are downloaded.
That means p = 0.03
and n = 75
By the Central Limit Theorem
Mean = μ = p = 0.03
Standard deviation = [tex]s = \sqrt{\frac{p(1-p)}{n} }[/tex]
[tex]s = \sqrt{\frac{(0.03)(0.97)}{75} }[/tex]
[tex]s=0.0197[/tex]
Hence,
In terms of the percentage of downloaded books, the sampling distribution's mean is 0.03 and its standard deviation is 0.0197.
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