Suppose that x has a binomial distribution with n = 50 and p = .6, so that ? = np = 30 and ? = sqrt( np(1 - p) ) = 3.4641. Calculate the following probabilities using the normal approximation with the continuity correction. (Hint: 23 < x < 33 is the same as 24 ? x ?32. Round your answers to four decimal places.)
(a) P(x = 30)
(b) P(x = 23)
(c) P(x ? 23)
(d) P(23 ? x ? 33)
(e) P(23 < x < 33)