Loretta, who turns eighty this year, has just learned about blood pressure probl

Question

Loretta, who turns eighty this year, has just learned about blood pressure problems in the elderly and is interested in how her blood pressure compares to those of her peers. Specifically, she is interested in her systolic blood pressure, which can be problematic among the elderly. She has uncovered an article in a scientific journal that reports that the mean systolic blood pressure measurement for women over seventy-five is mmHg, with a standard deviation of mmHg. Assume that the article reported correct information. Complete the following statements about the distribution of systolic blood pressure measurements for women over seventy-five.

(a) According to Chebyshev's theorem, at least 36% of the measurements lie between___ mmHg and ___ mmHg . (Round your answer to 1 decimal place.)

(b) According to Chebyshev's theorem, at least (56%, 75%, 84%, 89%) of the measurements lie between 121.8 mmHg and 146.6 .

(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately (68%,75%,95%,99.7%) of the measurements lie between 121.8 mmHg and 146.6

(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 99.7% of the measurements lie between ___ mmHg and ___mmHg .

Explanation / Answer

I think you have forgot to mention mean and stdev in the question. But I will guide you to solve it. It' easy.

a. 1-1/k^2 = .36 <-- chebeslev' formula for area under k stanadard deviations

1/k^2 = .64

k^2 = 1/.64

k = 1/.8 = 5/4 = 1.25

So, 36% of measurements lie within +/- 1.25 stdev of mean, so , CI is Mean +/- 1.25*Stdev will cover 36% area

b. So, 121.8 and 146.6, mean is is 134.2. Now it is not given if 134.2-121.6 = 9.6

Standard deviation is not given . So, By Chebyshev' , if 121.8 and 146.6 is k deviations away then 1-1/k^2 = 56%/75%/84%/89%.

- 56% - 1- 1k^2 = 56%

k = sqrt(1/.44) = 1.51

If it the range has 1.51 deviations, then k = 1.51 and therefore answer will be 56%.

Similarly, for 75%, k = 2,

for 84% , k = 2.5

for 89% , k = 3

So, answer will be Mean +/- k*Stdev as per the k value we find out above

c) Similarly, for k = 1,1.15, 2, or 3 we have (68%,75%,95%,99.7%). Accordingly, Mean - k*Stdev to Mean + k*Stdev is the answer

d) The bell shaped curve , with stdev of 3 we cover 99.7% of area around mean. So ,the measurements lie between Mean-3*Stdev mmHg and Mean +3*Stdev mmHg

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