Survey

Survey

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Let X be a normal random variable with mean 410 and standard deviation 40. Find Pr[360<X<440 ]. Give answer as a decimal number correct to two decimal places. Solution: We have to X-scores in our question that we have to convert to Z-scores. We do this by using the Z-Conversion formula for each one: Z X We are given 410 and 40 Converting 360 to a Z we get: 360 410 1.25 40 Converting 440 to a Z we get: 440 410 0.75 40 So, our problem now becomes Pr[1.25 Z 0.75] We can solve this problem by using the Normal Approximation Table (Appendix B in the text). First look up Z = 0.75. Now, look up Z = -1.25 It says .7734 It says .1056 So, our answer is .7734 — .1056 = .6678