Answer:
(a)Approximately 99.7% of women over 70 have blood pressures between 104 mmHg and 158 mmHg.
(b)Approximately 68% of women over 70 have blood pressures between 122 mmHg and 140 mmHg.
Explanation:
Given:
• Mean = 131 mmHg
,• Standard Deviation = 9 mmHg.
By the empirical rule, in a normal distribution:
• 68% of the data falls within one standard deviation.
,• 95% percent within two standard deviations, and
,• 99.7% within three standard deviations from the mean.
(a)
As given by the empirical rule above, 99.7% of data in a normal distribution falls within three standard deviations from the mean. That is:
[tex]\mu\pm3\sigma[/tex]Substitute the given values:
[tex]\begin{gathered} 131\pm3(9)=131\pm27 \\ =(131-27,131+27) \\ =(104,158) \end{gathered}[/tex]Approximately 99.7% of women over 70 have blood pressures between 104 mmHg and 158 mmHg.
(b)As given by the empirical rule above, 68% of data in a normal distribution falls within one standard deviation from the mean. That is:
[tex]\mu\pm\sigma=(131-9,131+9)=(122,140)[/tex]Approximately 68% of women over 70 have blood pressures between 122 mmHg and 140 mmHg.