Normal Distribution Homework PDF

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Normal Distribution Homework...

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Normal Distribution Homework

Systolic blood pressure in healthy adults has a normal distribution with mean 112 mmHg and standard deviation 10 mmHg. Abnormally high systolic blood pressure seriously raises the risks of heart attack and stroke. Abnormally low blood pressure (< 2 standard deviations below the mean) can also raise the risk of fainting and falls and may indicate severe dehydration.

You want to suggest that patients with high blood pressure seek treatment. If high blood pressure is considered to be 2 standard deviations above the mean, what is the minimum blood pressure that would be considered high and in need of treatment? 2= (X – 112)/10

X = 132

A person has a blood pressure of 89 following surgery. Would this be considered abnormal? Z = (89 – 112)/10 = -2.3. Following the 68-95-99 rule, 95% of observations will be within +/2 SD of the mean. This means that less than 2.5% is in the negative tail, or that probably less than 2% of people have a z-score smaller than -2.3 (blood pressure smaller than 89). This value would be considered abnormal and may indicate a problem like dehydration.

A person runs a marathon and has a blood pressure of 95 afterwards. Would you be concerned that this person is at risk of fainting? About what percentage of people would be expected to have a blood pressure lower than 95? Z = (95 – 112)/10 = -1.7. We know that 84% of people have blood pressures higher than Z=-1, so this person does deviate quite a bit from the norm, but not as dramatically as the previous example (this person is not in the 2.5% negative tail). This person is probably okay, but may need to drink some water slowly. To estimate the percentile, we know that 13.5% of the data lies within Z = -1 and Z=-2 and that 2.5% is below Z= -2. The z-score of -1.7 is closer to -2 than it is to -1, so we can assume that substantially less than half of the 13.5% is to the left of Z=-1.7. To estimate the percentile, we can do: 2.5 (% to left of Z= -2) + .2*13.5% (about 20% of the 13.5% is to the left) = about 5% have a value lower than this person.

About what percentage of the healthy population would you expect to have a blood pressure >135 mmHg? Z = (135-112)/10 = 2.3. Less than 2% of the healthy population would have a higher blood pressure > 135, so people with values in this range could probably benefit from treatment.

About what percentage of the healthy population would you expect to have a blood pressure >112 mmHg? 112 is the mean, so 50% of people would be above this value and 50% would be below. 112 represents the 50th percentile.

About what percentage of the healthy population would you expect to have a blood pressure >124 mmHg? Z = (124 – 112)/10 = 1.2. Z of 1 represents the 84th percentile, so probably about 88% of people have blood pressure >124 mmHg....