Question

The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of 121 and standard deviation of 20 .Someone qualifies as having Stage 2 high blood pressure if their systolic blood pressure is 160 or higher.a. Around what percentage of adults in the USA have stage 2 high blood pressure? Give your answer rounded to two decimal places. %

Answer 1

For a normal distribution, the standard score is given by the formula:

$\begin{gathered} z=\frac{x-\mu}{\sigma} \\ z\colon\text{standard score} \\ x\colon\text{observed score} \\ \mu\colon\operatorname{mean}\text{ of the sample} \\ \sigma\colon\text{standard deviation of the sample} \end{gathered}$

From the question, we are provided with the following information:

$\begin{gathered} x=160 \\ \mu\colon121 \\ \sigma\colon20 \end{gathered}$

Thus, we have:

$\begin{gathered} z=\frac{160-121}{20} \\ z=\frac{39}{20} \\ z=1.95 \end{gathered}$

Probability of z>1.95 is 0.02558 or 2.558%

Hence, the percentage of adults in the USA that have stage 2 high blood pressure is 2.558%