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 131.5mmHg, with a standard deviation of 5.7mmHg.

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 ?56%75%84%89% of the measurements lie between 117.25 mmHg and 145.75 mmHg. (b) According to Chebyshev's theorem, at least ?56%75%84%89% of the measurements lie between 120.1 mmHg and 142.9 mmHg. (c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately ?68%75%95%99.7% of the measurements lie between 120.1 mmHg and 142.9 mmHg. (d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the measurements lie between mmHg and mmHg .

Answer 1

Solution-:

mean-ksd=117.25

mean+ksd=145.75

But mean=131.5

sd=5.7

so k=131.5-117.25/5.7

k=2.5

according to chebyshev's 1-1/k^2 =1-1/2.5^2=0.84*100=84%  the minimum percentage of data between 117.25 and 145.75

84%

Solution-b:

mean-ksd=120.1

mean+ksd=142.9

But mean=131.5

sd=5.7

so k=131.5-120.1/5.7

k=2

according to chebyshev's 1-1/2^2 =1-1/4=0.75*100=75%  the minimum percentage of data between 120.1 and 142.9

75%

Solution-c:

(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately ?68%75%95%99.7% of the measurements lie between 120.1 mmHg and 142.9 mmHg.

according to empirical rule 95% of the value lies in between 131.5-2*5.7=120.1 and 131.5+2*5.7=142.9

ANSWER;

95%

Solution-d:

68% of the values lies in between mean-sd and mean+sd that is between 131.5-5.7 = 125.8 and 131.5+5.7=137.2

According to the empirical rule, approximately 68% of the measurements lie between 125.8 mmHg and 137.2 mmHg
.