Step 1 :Given that the proportion of green newts, denoted as p, is 0.45 and the sample size, denoted as n, is 134.
Step 2 :The mean of the normal distribution is the expected proportion of green newts, which is 0.45.
Step 3 :The standard deviation can be calculated using the formula for the standard deviation of a sample proportion, which is \(\sqrt{p(1-p)/n}\), where p is the proportion of green newts and n is the sample size. Substituting the given values, we get the standard deviation as approximately 0.043.
Step 4 :The left box is 2 standard deviations below the mean, the middle box is the mean, and the right box is 2 standard deviations above the mean.
Step 5 :Calculating these values, we get the left box as approximately 0.36, the middle box as 0.45, and the right box as approximately 0.54.
Step 6 :Final Answer: The values for the boxes are approximately \(\boxed{0.36}\), \(\boxed{0.45}\), and \(\boxed{0.54}\), respectively.