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 133.8 mmHg, with a standard deviation of 6.3 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 8/9 (about 89%) of the measurements lie between mmHg and mmHg. (Round your answer to 1 decimal place.) V of the measurements (b) According to Chebyshev's theorem, at least 2 lie between 121.2 mmHg and 146,4 mmHg. х 5 ? (c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 2 V of the measurements lie between 121.2 mmHg and 146,4 mmHg, (d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the measurements lie between ImmHg and mmHg

Answer 1

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Dist params

Mean = 133.8 mmHg

Stdev = 6.3 mmHg

a. Chebyshev's theorm states that k deviations from mean covers at least 1-1/k^2 area

So, 1-1/k^2 = 8/9
1/k^2 = 1/9
k = +3

So, measurement lie between 133.8 mgHg +/- 3*6.3 mmHg

= 114.9 mmHg to 152.7 mmHg

Answer: 114.9 mmHg and 152.7 mmHg

b.

121.2 and 146.4 are 2 deviations from mean.

So, according to Chebeshev' theorm it covers at least 1 - 1/2^2 = 3/4 or 75% of the measurements

Answer: According to Chebeshev' therom at least 75% of the measrements lie betwee n121.2 mmHg and 146.4 mmHg

c.

121.2 mmHg and 146.4 mmHg is basically 2 deviations from mean. So, by empirical rule of normal distribution 95% of the measurements lie between 121.2 mmHg and 146.4 mmHg.

Answer: between 121.2 mmHg and 146.4 mmHg.

d.

68% of measurements will be 1 deviation from mean.

So, that' 133.8 +/- 6.3 mmHg

= 127.5 to 140.1

Answer: 68% of the measurements lie between 127.5 mmHg and 140.1 mmHg