Draw some pictures. Consider the binomial setting with n = 50 and p = 0.4.
(a) The sample proportion p^ will have a distribution that is approximately Normal. Give the mean and the standard deviation of this Normal distribution.
(b) Draw a sketch of this Normal distribution. Mark the location of the mean.
(c) Find a value p* for which the probability is 95% that p^ will be between ±p*. Mark these two values on your sketch.