Question

systolic blood pressure readings for a population of adults are normally distributed with a mean of 117 and a standard deviation of 10. (a reading above 140 is considered to be high blood pressure.) begin by converting the given blood pressure reading into a z - score. then use the accompanying table of z - scores and percentiles to find the percentage of people with blood pressure readings above 116. click the icon to view the table of z - scores and percentiles. the z - score is - 0.1. (type an integer or a decimal.) the percentage of people with blood pressure readings above 116 is % (round to two decimal places as needed.)

Explanation:

Step1: Recall z - score formula

The z - score formula 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. We are given $\mu = 117$, $\sigma=10$, and $x = 116$. The z - score $z=\frac{116 - 117}{10}=\frac{-1}{10}=- 0.1$.

Step2: Use the z - score table

The z - score table gives the cumulative probability $P(Z\lt z)$. Looking up $z=-0.1$ in the z - score table, we find that $P(Z\lt - 0.1)=0.4602$.

Step3: Calculate the probability of $Z\gt - 0.1$

We know that $P(Z\gt z)=1 - P(Z\lt z)$. So, $P(Z\gt - 0.1)=1 - 0.4602 = 0.5398$.

Answer:

$53.98$