Step 1 :Given that the proportion of green newts, p, is 0.35 and the sample size, n, is 213.
Step 2 :We are asked to find the mean and standard deviation of the proportion of green newts in the sample.
Step 3 :The mean of a proportion is simply the proportion itself, so the mean is \(\boxed{0.35}\).
Step 4 :The standard deviation of a proportion can be calculated using the formula \(\sqrt{p(1-p)/n}\), where p is the proportion and n is the sample size.
Step 5 :Substituting the given values into the formula, we get the standard deviation as \(\sqrt{0.35(1-0.35)/213} = 0.032681418533639144\).
Step 6 :The question also asks for two standard deviations below and above the mean. This can be calculated as mean - 2*std_dev and mean + 2*std_dev respectively.
Step 7 :Calculating these values, we get two standard deviations below the mean as \(0.35 - 2*0.032681418533639144 = \boxed{0.28}\) and two standard deviations above the mean as \(0.35 + 2*0.032681418533639144 = \boxed{0.42}\).