The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mm Hg and a standard deviation of 12 mm Hg. What percentage of 18-year-old women have a systolic blood pressure that is within 3 standard deviations of the mean on either side?

Question

The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mm Hg and a standard deviation of 12 mm Hg. What percentage of 18-year-old women have a systolic blood pressure that is within 3 standard deviations of the mean on either side?

Apply the 68-95-99.7 rule to this question.

A. 68%
B. 95%
C. 100%
D. 99.7%

Answer :D

Answer 1

I used the actual normal distribution and got

.9973

http://davidmlane.com/normal.html

Answer 2

I used the actual normal distribution and got

.9973

http://davidmlane.com/normal.html

Answer 3

To answer this question, we can use the 68-95-99.7 rule, also known as the empirical rule or the three-sigma rule. This rule helps us estimate the percentage of observations that fall within a certain number of standard deviations from the mean in a normal distribution.

According to the 68-95-99.7 rule:
- Approximately 68% of the observations fall within one standard deviation of the mean.
- Approximately 95% of the observations fall within two standard deviations of the mean.
- Approximately 99.7% of the observations fall within three standard deviations of the mean.

In this case, we want to find the percentage of 18-year-old women with a systolic blood pressure that is within 3 standard deviations of the mean on either side. The mean is 120 mm Hg and the standard deviation is 12 mm Hg.

To find the range within three standard deviations of the mean, we multiply the standard deviation by 3 and add/subtract it to/from the mean:
Upper range = mean + (3 * standard deviation)
Lower range = mean - (3 * standard deviation)

Upper range = 120 + (3 * 12) = 120 + 36 = 156 mm Hg
Lower range = 120 - (3 * 12) = 120 - 36 = 84 mm Hg

Thus, the range within three standard deviations of the mean is from 84 mm Hg to 156 mm Hg.

To find the percentage of 18-year-old women with a systolic blood pressure within this range, we can use the 99.7% value from the 68-95-99.7 rule. Since this rule tells us that approximately 99.7% of the observations fall within three standard deviations of the mean, the answer is D. 99.7%.

The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mm Hg and a standard deviation of 12 mm Hg. What percentage of 18-year-old women have a systolic blood pressure that is within 3 standard deviations of the mean on either side?

I used the actual normal distribution and got

I used the actual normal distribution and got

Thanks

To answer this question, we can use the 68-95-99.7 rule, also known as the empirical rule or the three-sigma rule. This rule helps us estimate the percentage of observations that fall within a certain number of standard deviations from the mean in a normal distribution.