A blood pressure test was given to 450 women ages 20 to 36. It showed that their mean systolic blood pressure was 118.6 mm Hg, with a standard deviation of 12.0 mm Hg.(a) Determine the z-score, to the nearest hundredth, for a woman who had a systolic blood pressure reading of 112.0 mm Hg.
Question
A blood pressure test was given to 450 women ages 20 to 36. It showed that their mean systolic blood pressure was 118.6 mm Hg, with a standard deviation of 12.0 mm Hg.(a) Determine the z-score, to the nearest hundredth, for a woman who had a systolic blood pressure reading of 112.0 mm Hg.
Solution
To calculate the z-score, we use the formula:
z = (X - μ) / σ
where: X = individual score (in this case, the blood pressure reading of the woman) μ = mean of the population (in this case, the mean systolic blood pressure of the women) σ = standard deviation of the population (in this case, the standard deviation of the systolic blood pressure of the women)
Substituting the given values into the formula:
z = (112.0 - 118.6) / 12.0
z = -6.6 / 12.0
z = -0.55
So, the z-score for a woman who had a systolic blood pressure reading of 112.0 mm Hg is -0.55, to the nearest hundredth. This means her blood pressure is 0.55 standard deviations below the mean blood pressure of the group of women.
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