Question

Suppose that the mean systolic blood pressure for women over age seventy is 131 mmHg (millimeters of mercury), with a standard deviation of 9 mmHg. Suppose that the blood pressures are normally distributed.

(a) Approximately _____ of women over seventy have blood pressures between 113 mmHg and 149 mmHg.

(b) Approximately 99.7%
of women over seventy have blood pressures between _____ mmHg and _____ mmHg.

Answer 1

To find the probability that women have blood pressures between 113 mmHg and 149 mmHg, we need to standardize the values using z-scores and find the respective probabilities. Approximately 99.7% of women over seventy have blood pressures between 113 mmHg and 149 mmHg.

Step-by-step explanation:

(a) To find the probability that women have blood pressures between 113 mmHg and 149 mmHg, we first need to standardize the values using z-scores. The z-score formula is given by z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

For 113 mmHg: z = (113 - 131) / 9 = -2
For 149 mmHg: z = (149 - 131) / 9 = 2

Using a z-table, we can find the respective probabilities associated with these z-scores. The probability of having a blood pressure between 113 mmHg and 149 mmHg is the sum of the probabilities to the left of 113 mmHg and to the right of 149 mmHg.

(b) Approximately 99.7% of women over seventy have blood pressures between 113 mmHg and 149 mmHg. This is because within 3 standard deviations of the mean, approximately 99.7% of the data would fall.