Let 0< α< 1. For a normally distributed variable, show that 100(1 − α)% of all possible observations lie within zα/2 standard deviations to either side of the mean, that is, between μ − zα/2 • σ and μ + zα/2 • σ.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
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Let 0< α< 1. For a normally distributed variable, show that 100(1 − α)% of all possible observations lie within zα/2 standard deviations to either side of the mean, that is, between μ − zα/2 • σ and μ + zα/2 • σ.

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