Question

question 4 of 10 > according to a health information website, the distribution of adults diastolic blood pressure (in millimeters of mercury) can be modeled by a normal distribution with mean 70 and standard deviation 20. diastolic blood pressures higher than 120 are classified as a hypertensive crisis and require emergency medical attention. what percent of adults have a diastolic bp that is classified as a hypertensive crisis? round your answer to 4 decimal places and then convert to a percentage.

Explanation:

Step1: Calculate the z - score

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 120$ (the value of interest), $\mu = 70$ (the mean), and $\sigma=20$ (the standard deviation). So, $z=\frac{120 - 70}{20}=\frac{50}{20}=2.5$.

Step2: Find the probability

We want to find $P(X>120)$, which is equivalent to $P(Z > 2.5)$ in the standard normal distribution. Since the total area under the standard - normal curve is 1, and $P(Z>z)=1 - P(Z\leq z)$. Looking up $P(Z\leq2.5)$ in the standard normal table, we find that $P(Z\leq2.5)=0.9938$. So, $P(Z > 2.5)=1 - 0.9938 = 0.0062$.

Step3: Convert to percentage

To convert the probability to a percentage, we multiply by 100. So the percentage is $0.0062\times100 = 0.6200\%$.

Answer:

0.6200%