Consider random samples of size 50 from a population with proportion 0.30 . Find the standard error of the distribution of sample proportions.

Round your answer for the standard error to three decimal places.
standard error $=$
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Step 1 ：We are given a population with proportion \(P = 0.30\) and we are considering random samples of size \(n = 50\).

Step 2 ：We are asked to find the standard error of the distribution of sample proportions.

Step 3 ：The formula for the standard error of the distribution of sample proportions is given by \(SE = \sqrt{\frac{P \cdot (1 - P)}{n}}\), where \(P\) is the population proportion and \(n\) is the sample size.

Step 4 ：Substituting the given values into the formula, we get \(SE = \sqrt{\frac{0.3 \cdot (1 - 0.3)}{50}}\).

Step 5 ：Calculating the above expression, we find that \(SE = 0.0648074069840786\).

Step 6 ：Rounding this to three decimal places, we get \(SE = 0.065\).

Step 7 ：Final Answer: The standard error of the distribution of sample proportions is \(\boxed{0.065}\).