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Precalculus Mathematics Homework Help
Statistics problem using cumulative from mean
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[QUOTE="Ray Vickson, post: 5143889, member: 330118"] No, absolutely not! There IS no upper limit! The fact that you have a normal distribution table that stops at z = 3.09 is irrelevant; larger tables (or computer software) could go much higher than z = 3.09. In this problem the upper limit does not exist: your z-table implies that ##P(Z \leq 1.88) = 0.9699##, which means that ##P(Z > 1.88) = 1 - 0.9699 = 0.0301##. In fact, using software we can find more accurate results, which are [tex] P(1.88 \leq Z \leq 3.09) = 0.0290532565\\ P(Z \geq 1.88) = .0300540390 [/tex] These are not the same; they differ by the amount ##P(Z > 3.09) = 0.0010007825##. [B]Note added in edit:[/B] of course, the Pb concentration cannot go to ##\infty## (or to negative values) in the real world, but that just means that the normal distribution does not apply to very high or very low concentrations. In particular, an actual upper bound must be obtained from physiology and chemistry and cannot just be obtained from a statistical table. The normal distribution---as an approximation to reality---cannot be expected to apply with any accuracy outside a central range, but we would need a lot more information in order to assess the actual range of approximate applicability. [/QUOTE]
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Statistics problem using cumulative from mean
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