An educational study to be conducted requires a test score inthe middle 40% rang

Question

An educational study to be conducted requires a test score inthe middle 40% range. If = 100 and = 15, find the highest and lowest acceptable testscores that would enable a canidate to participate in the study.Assume the variable is normally distributed. The answer I got is different from the answer given in thebook. The book says the answer is 92.2 - 107.8 This is what I did. I don't know where I went wrong. Area of 0.2000 is z=0.793( from the z chart) So, x1 = z +      = (0.793)(15) + 100      = 11.895 + 100     = 111.895 x2 = (-0.793)(15) + 100     = 88.105 So, An educational study to be conducted requires a test score inthe middle 40% range. If mu = 100 and sigma = 15, find the highest and lowest acceptable test scores that would enable a canidate to participate in the study. Assume the variable is normally distributed. The answer I got is different from the answer given in the book. The book says the answer is 92.2 - 107.8 This is what I did. I don't know where I went wrong. Area of 0.2000 is z=0.793( from the z chart) So, x1 = z sigma + mu = (0.793)(15) + 100 = 11.895 + 100 = 111.895 x2 = (-0.793)(15) + 100 = 88.105 So,

Explanation / Answer

You need to find the area of 0.3000 because that would be0.2000 away from .5000 .5000 - .3000 = .2000 This is for the lower bound. On my table, it's about -.523 The upper bound, as you know, would have a z-scoreof .523 Which gives you the area of .7000 100 + (-.523)(15) x 100 + (.523)(15) 92.155 x 107.845 Remember that the area that a z-score is everything equal toand less than the z number of standard distributions.

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