You are conducting a study on hypertension for which you have recruited 60 African-American adults. If the biostatistician for your study informs you that the sample population of your study is approximately normal, the mean systolic blood pressure is 140 mmHg, and the standard deviation is 7 mmHg, how many participants would you expect to have a systolic blood pressure between 126 and 154 mmHg?
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- 10 participants
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- 41 participants
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- 57 participants
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- 68 participants
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- Not enough information provided
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EXP:
In a normally distributed sample 95% of the observations are expected to fall within 2 standard deviations of the mean.
The utility of using normal curves in biostatistics is the ability to rely on certain characteristics of the normal distribution (see Rosner, below). Because this sample’s standard deviation is 7 mmHg, the values of 154 and 126 mmHg are each 2 standard deviations above and below the mean of 140 mmHg, e.g. (154-140)/7 = 2. Because the sample is normally distributed we can reasonably assume that 95% of the participants will fall within +/- 2 standard deviations of the mean, i.e. 0.95 x 60 = 57 participants.
Rosner defines one property of the normal distribution as such: 68%, 95%, and 99.7% of observations can be expected to fall within 1, 2, and 3 standard deviations respectively of the mean.
Illustration A depicts a normal distribution with +/- 1, 2, and 3 standard deviations (SDs) delineating the percentages under the curve.