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Chapter 6: Q8 (page 292)

In Exercises 6–10, assume that women have diastolic blood pressure measures that are normally distributed with a mean of 70.2 mm Hg and a standard deviation of 11.2 mm Hg (based on Data Set 1 “Body Data” in Appendix B).

Diastolic Blood Pressure Find P90, the 90th percentile for the diastolic blood pressure levels of women.

Short Answer

Expert verified

The 90th percentile for the blood pressure of women is 84.5 mm Hg.

Step by step solution

01

Given information

Diastolic blood pressure measures for women are normally distributed with a mean of 70.2 mm Hg and a standard deviation of 11.2 mm Hg.

02

Define the random variable

Let X be the random variable for the blood pressure of women.

Then,

X~Nμ,σ2~N70.2,11.22

03

Compute the z score corresponding to the 90th percentile

Let X=P90be the 90th percentile score with the corresponding zscore of such that

Thus, as per the definition of percentile,

z90=P90-μσ...1

In the standard normal table, the zscore 1.28 has the closest value of 0.8997 for the cumulative probability of 0.90.

PX<P90=PZ<z90=0.90

Thus,z90=1.28 .

04

Compute the 90th percentile

Substituting the zscore in equation (1),

1.28=P90-70.211.2P90=84.536

Thus, the 90th percentile is 84.5 mm Hg.

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