Question

suppose that the mean systolic blood pressure for women over age seventy is 134 mmhg (millimeters of mercury), with a standard deviation of 6 mmhg. suppose that the blood pressures are normally distributed. complete the following statements.
(a) approximately? of women over seventy have blood pressures between 116 mmhg and 152 mmhg.
(b) approximately 68% of women over seventy have blood pressures between mmhg and mmhg.

Explanation:

Step1: Calculate the number of standard deviations for part (a)

For \(116\): \(z_1=\frac{116 - 134}{6}=\frac{- 18}{6}=-3\)
For \(152\): \(z_2=\frac{152 - 134}{6}=\frac{18}{6}=3\)
By the empirical rule (68 - 95 - 99.7 rule), approximately \(99.7\%\) of the data lies within \(z=-3\) and \(z = 3\) in a normal distribution.

Step2: Calculate the values for part (b)

By the empirical rule, approximately \(68\%\) of the data lies within \(z=-1\) and \(z = 1\) in a normal distribution.
For \(z=-1\): \(x_1=\mu+z\sigma=134+( - 1)\times6=134 - 6 = 128\)
For \(z = 1\): \(x_2=\mu+z\sigma=134+1\times6=134 + 6=140\)

Answer:

(a) Approximately \(99.7\%\) of women over seventy have blood pressures between \(116\) mmHg and \(152\) mmHg.
(b) Approximately \(68\%\) of women over seventy have blood pressures between \(128\) mmHg and \(140\) mmHg.