Question

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. a healthy diastolic pressure for an adult is less than 80. about what proportion of adults have healthy diastolic blood pressures? round your answer to 4 decimal places.

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value from the data set, $\mu$ is the mean and $\sigma$ is the standard deviation. Here, $\mu = 70$, $\sigma=20$ and we want to find the proportion for $x < 80$. So, $z=\frac{80 - 70}{20}=\frac{10}{20}=0.5$.

Step2: Find the proportion from the standard normal table

We look up the z - score of 0.5 in the standard - normal distribution table (the cumulative distribution function $\varPhi(z)$). The value corresponding to $z = 0.5$ in the standard - normal table is approximately 0.6915.

Answer:

0.6915