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 133.5 mmHg, with a standard deviation of 6.1 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.) (6) According to Chebyshev's theorem, at least? of the measurements lie between 121.3 mmHg and 145.7 mmHg. ? X (c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately? of the measurements lie between 121.3 mmHg and 145.7 mmHg. (d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 99.7% of the measurements lie between mmHg and mmHg.

Answer 1

Sol:

1-1/k^2=0.36

1-0.36=1/k^2

0.64=1/k^2

k^2=1/0.64

k= 1.25

mean-k*sd,mean+k*sd

133.5-1.25*6.1 and 133.5+1.25*6.1

125.875 and 141.125

ANSWER(A)

According to chebyshev's theorem,atleast 36% of the measurements lie between 125.9 and 141.1 mm Hg

Solution-b:

mean-k*sd=121.3

mean+k*sd=145.7

we have

mean=133.5

sd=6.1

substitute in eq(2)

k=(145.7-133.5)/6.1

k=2

Atleast

1-1/2^2=1-1/4=0.75=0.75*100=75%

ANSWER(B)

Atleast 75% of the measurments lie between 121.3 mmHg and 145.7 mm Hg

Solution-c:

According to empirical rule 68% of the values lie between mean -sd and mean+sd

133.5-6.1 and 133.5+6.1

127.4 and 139.6

95% of the values lie between mean- 2*sd and mean+2*sd

133.5-2*6.1 and 133.5+2*6.1

121.3 and  145.7

99.7% of the values lie between mean -3sd and mean+3*sd

133.5-3*6.1 and 133.5+3*6.1

115.2 and  151.8

ANSWER(C)

95% of the values lie between mean- 2*sd and mean+2*sd

121.3 and  145.7

95% of the measurements lie between  121.3 and  145.7

Solution(d)

99.7% of the values lie between mean -3sd and mean+3*sd

115.2 and  151.8

ANSWER:

99.7% of the measurments lie between  115.2 and  151.8 mm Hg