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Problem 8. (4 points) The Normal and Binomial distributions share a special relationship in that the Normal distribution approximates the Binomial distribution if the number of trials is large and the probability of \"success" is not too close to 0 or 1. That is, if X ~ binomial(n, p) and Y ~ N (u x , oi). where x is the mean of X and a: is the variance of X . then P(X g z) z P(Y g :1: + 0.5). The \"+ 0.5\" above is called the continuity correction and is needed since a continuous distribution is approximating a discrete distribution. Let X ~ binomial (1000, 0.45). Use the Normal approximation with the continuity correction to nd P(400 S X S 600). Show all your work. including any calculator functions you use, and round your nal answer to ve decimal places