Areas under normal distribution curves can be used calculate probabilities of many random variables in thenatural and social sciences.The graph of the Standard Normal Curve, with a mean of 0 and a standard deviation of 1 is given below,and its function is given by1f(x) =√2Te1The integral ofe dx would be used to calculate the probability of an event that occurs√2T-1.5between -1.5 to 1.5 standard deviations from the mean.(-1.5, 0.13)1Unfortunately,√2π -1.5methods to approximate the values.1.5-1.51.5(-1, 0.24)Using Simpson's Rule,(-0.5, 0.35)e dx has no proper closed form antiderivative, so we must use numerical1.5-1.51-0.5-0-2Using the Midpoint Rule with three rectangles of equal width,dx0Using the Trapezoidal Rule with six trapezoids of equal width,(0, 0.4)0.5Round answers to 4 decimal places when appropriate.(0.5, 0.35)(1, 0.24)1.5Ibe1.51.5[ 13 e-t de = \е1.5e-2е dx(1.5, 0.13)

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Answered: Areas under normal distribution curves…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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