Suppose that the mean systolic blood pressure for women over age seventy is 132 mmHg (millimeters of mercury), with a standard deviation of 9 mmHg. Suppose that the blood pressures are normally distributed. Complete the following statements.(a) Approximately 68% of women over seventy have blood pressures between mmHg and mmHg.(b) Approximately of women over seventy have blood pressures between 105 mmHg and 159 mmHg.
Question
Suppose that the mean systolic blood pressure for women over age seventy is 132 mmHg (millimeters of mercury), with a standard deviation of 9 mmHg. Suppose that the blood pressures are normally distributed. Complete the following statements.(a) Approximately 68% of women over seventy have blood pressures between mmHg and mmHg.(b) Approximately of women over seventy have blood pressures between 105 mmHg and 159 mmHg.
Solution
(a) The 68% range for a normal distribution is defined by the mean plus and minus one standard deviation. In this case, the mean is 132 mmHg and the standard deviation is 9 mmHg. Therefore, approximately 68% of women over seventy have blood pressures between 132 - 9 = 123 mmHg and 132 + 9 = 141 mmHg.
(b) The range of 105 mmHg to 159 mmHg is defined by the mean plus and minus three standard deviations. In this case, the mean is 132 mmHg and the standard deviation is 9 mmHg. Therefore, 132 - 39 = 105 mmHg and 132 + 39 = 159 mmHg. According to the empirical rule (or 68-95-99.7 rule) for normal distributions, approximately 99.7% of women over seventy have blood pressures between 105 mmHg and 159 mmHg.
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