Question

Suppose the systolic blood pressure (in mm) of adult males has an approximately normal distribution with mean μμ =125 and standard deviation σσ =14.

Create an empirical rule graph with the following:

• A title and label for the horizontal axis including units.
• Vertical lines for the mean and first 3 standard deviations in each direction with numerical labels on the horizontal axis
• Labels for the areas of the 8 regions separated by the vertical lines as well.

Note: This may be hand drawn or computer generated. See the models for desired formats.

a. Upload your completed file below.

Now use your graph to answer the following questions.

b. About 99.7% of men will have blood pressure between what amounts?

and

c. What percentage of men will have a systolic blood pressure outside the range 97 mm to 139 mm?

d. Suppose you are a health practitioner and an adult male patient has systolic blood pressure of 170 mm. Use statistics to explain the gravity of his situation. Write an essay below that includes the following:

1. A brief description of the normal distribution.
2. Why the normal distribution might apply to this situation.
3. Describe the specific normal distribution for this situation (give the mean and standard deviation)
4. A brief description of the empirical rule
5. What region of the graph (drawn in part a) the individual falls in
6. An estimate of individual's percentile.
7. Why this signifies a health concern.
8. A suggested course of action.

Answer 1

Mean = u = 125

Std. deviation = s = 14

Range within 1 standard deviation of mean

u + s = 139

u - s = 111

Range within 2 standard deviation of mean

u + 2s = 153

u - 2s = 97

Range within 3 standard deviations of mean

u + 3s = 167

u - 3s = 83

b. According to empirical rule

99.7% of the data would fall between 3 standard deviations of the mean.

u + 3s = 167

u - 3s = 83

83 and 167

C.

P( 97 < X < 139 ) = 0.8186 = 81.86%

D.

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In graph form, normal distribution will appear as a bell curve.

The empirical rule or the three-sigma rule or 68-95-99.7 rule states that for a normal distribution, almost all data falls within three standard deviations (s) of the mean (denoted by u). The empirical rule shows that 68% falls within the first standard deviation (u ± s), 95% within the first two standard deviations (u ± 2s), and 99.7% within the first three standard deviations (u ± 3s).

We can observe, u + 3s = 167,

The value 170 which is more than 3 standard deviations away from mean would be considered as an extreme value.

As we can observe the value of 170 is the 99.93th Percentile

Since the value of 170 corresponds to an extreme value in the distribution which would mean the blood pressure is unsually high and a bad indicator of the health of the individual.