Question

systolic blood pressure readings for a population of adults are normally distributed with a mean of 123 and a standard deviation of 16. (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 below 155. click the icon to view the table of z - scores and percentiles. the z - score is 2. (type an integer or a decimal.) the percentage of people with blood pressure readings below 155 is %. (round to two decimal places as needed.)

Explanation:

Step1: Calculate the z - score formula

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 155$, $\mu=123$, and $\sigma = 16$.
$z=\frac{155 - 123}{16}$

Step2: Simplify the z - score calculation

$z=\frac{32}{16}=2$

Step3: Find the percentage using the z - score table

Looking up the z - score of 2 in the z - score and percentile table, the area to the left of $z = 2$ (which represents the percentage of people with blood - pressure readings below 155) is 0.9772. To convert this to a percentage, we multiply by 100.
$0.9772\times100 = 97.72\%$

Answer:

The z - score is 2.
The percentage of people with blood pressure readings below 155 is 97.72%