Question

systolic blood pressure readings for a population of adults are normally distributed with a mean of 120 and a standard deviation of 12. (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 144. click the icon to view the table of z - scores and percentiles. the z - score is. (type an integer or a decimal.) the percentage of people with blood pressure readings below 144 is %. (round to two decimal places as needed.)

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 144$, $\mu=120$, and $\sigma = 12$.
$z=\frac{144 - 120}{12}=\frac{24}{12}=2$

Step2: Find the percentage using the z - score table

Looking up the z - score of 2 in the standard normal distribution (z - score) table, the area to the left of $z = 2$ represents the percentage of people with blood - pressure readings below 144. The value corresponding to $z = 2$ in the table is 0.9772. To convert this to a percentage, we multiply by 100. So the percentage is $0.9772\times100 = 97.72\%$

Answer:

The z - score is 2.
The percentage of people with blood pressure readings below 144 is 97.72%