A geriatric psychologist is interested in studying nonpharmacological approaches

Question

A geriatric psychologist is interested in studying nonpharmacological approaches for senior citizens struggling with prehypertension. Systolic blood pressure scores for senior citizens follow a normal distribution with -110 and -21. Use the Distributions tool to help answer the questions that follow Note: To find the probability above or below a z-score, click on the normal curve icon with one line, and position the line at the appropriate z-score on the horizontal axis. The areas under the standard normal curve above and below the z-score will be displayed to the left and right of the vertical line, respectively. To find the probability between two z-scores, click on the normal curve icon with two lines, and position the left line at the lower z-score and the right line at the higher z-score. The area under the normal curve between the vertical lines will be displayed in blue Standard Normal Distribution Mean -0.0 Standard Deviation 1.0 -3 -2 -1 3 The highest possible z-score that is still in the lowest 80% of the systolic blood pressure distribution is z- Use this z-score to determine X, the corresponding systolic blood pressure score.

Explanation / Answer

the highest possible z score that is still in the lowest 80%.. is z =~ 0.84

X =mean +z*std deviation =110+0.84*21=127.64 ( please try 127.67 if this comes wrong)

the score X is the 80th percentile of systolic.... the percentile rank of this score is 80.

% of senior citizen has systolic bolld pressure between 120 and 139=P(120<X<139)

=P(0.48<Z<1.38)=23.18%

% of senior citizen has systolic bolld pressure below 91 =P(X<91)=P(Z<-0.90)=18.41%

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