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Chapter 6: Q.6.115 (page 279)

Express thekth percentile, Pk, of a normally distributed variable in terms of its mean, μ, and standard deviation, σ.

Short Answer

Expert verified

Thek th percentile of a normally distributed variable in terms of mean (μ) and standard deviation (σ) isPk=zkσ+μ.

Step by step solution

01

Given Information

In standard normal distribution, the k th percentile represents the area under curve that fall below k% of the data.

02

Explanation

The area to the left of the zscore is k100Pk. Let the zscore be zk.

That is, Pz≤zk=Pk, Here the zscore is x-μσ

Hence,

z=x-μσ

zkσ=Pk-μ

Pk=zkσ+μ

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Most popular questions from this chapter

30. Northwest Atlantic Cod. Researchers M. Kroll et al. studied the influence of paternity on rates of mortality and development in eggs and larvae of Northwest Atlantic cod in the article, "Paternal Effects on Early Life History Traits in Northwest Atlantic Cod, Gadus morhua" (Journal of Applied Ichthyology, Vol. 29. Issue 3. pp. 623629). A sample of adult male Northwest Atlantic cod was collected in Nova Scotia, Canada. The following table gives the lengths, in centimeters (cm), of the cod sampled.

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