statistics
For a normal distribution with µ = 200 and ó = 50, what X values form the boundaries for the middle 60% of the distribution?
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The boundaries for the middle 60% of the distribution are the values X1 and X2, such that P(X1 < X < X2) = 0.60. For a normal distribution, these values can be found using the standard normal tables, as the points that are equidistant from the mean that encompass 0.60 of the total area under the curve. Using the standard normal tables, we find that X1 = 180 and X2 = 220, since P(-1 < Z < 1) = 0.60. Therefore, for the normal distribution with µ = 200 and ó = 50, the X values at the boundaries of the middle 60% of the distribution are X1 = 180 and X2 = 220.
