Question

use the empirical rule to answer the question below. the systolic blood pressure of 18 - year - old women is a roughly bell - shaped distribution with a mean of 120 mmhg and a standard deviation of 12 mmhg. what percentage of 18 - year - old women have a systolic blood pressure between 96 mmhg and 144 mmhg? (hint: a numberline might be useful.) a. approximately 68% b. at least 89% c. approximately 95% d. at least 75%

Explanation:

Step1: Recall the empirical rule

The empirical rule for a normal - distribution states that approximately 68% of the data lies within 1 standard deviation of the mean, approximately 95% lies within 2 standard deviations of the mean, and approximately 99.7% lies within 3 standard deviations of the mean.

Step2: Calculate the number of standard - deviations

The mean is $\mu = 120$ mmHg and the standard deviation is $\sigma=12$ mmHg. For the lower bound $96$ mmHg, we calculate $z_1=\frac{96 - 120}{12}=\frac{- 24}{12}=-2$. For the upper bound $144$ mmHg, we calculate $z_2=\frac{144 - 120}{12}=\frac{24}{12}=2$. So, the values $96$ mmHg and $144$ mmHg are 2 standard deviations below and above the mean respectively.

Step3: Apply the empirical rule

Since the values are 2 standard deviations from the mean, approximately 95% of the data lies between these two values according to the empirical rule.

Answer:

C. Approximately 95%