SOLUTION: 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. Speci

Question 1161133: 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 134.5 mmHg, with a standard deviation of 6.6 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 BLANK mmhg and BLANK mmHg. Round your answer to 1 decimal place
B) According to Chebyshev’s theorem, at least BLANK of the measurements lie between 121.3 mmHg and 147.7 mmHg.
C) Suppose that the distribution is bell-shaped. According to the empirical rule approximately BLANK of the measurements lie between 121.3 mmHg and 147.7 mmHg
D) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the measurements lie between BLANK mmHg and BLANK mmHg

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
start with c and d. They are easier
c-can be shown to be between -2 and +2 sd and that is 95% by the empirical rule.
d-68% is between -1 and +1 sd so that its between 134.5-6.6 or 127.9 mm Hg and 134.5+6.6 or 141.1 mm Hg
Chebyshev's between -2 and +2 sd (what c is) says that at least 1-(1/2^2) must be in this interval; it can be more but not fewer. This would be 3/4 of the measurements minimum or 75%.
For a:
36% is 1-(1/x^2), where x is the number of sds.
so 0.36=1-(1/x^2)
and (1/x^2)=0.64
(1/x)=0.8
.8x=1
x=1.25 sd
each sd is 6.6 mm Hg, so 1.25 of them are 8.25 mm Hg.
(126.25 mm Hg, 142.75 mm Hg) is the interval containing at least 36%, or to answer (126.3, 142.8)

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