explain please.

Question

The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of 120 and standard deviation of 16 .

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

A sketch looks like this:

You can see that the result you are looking for (blue shaded area) is very small.

Using a TI-84 calculator, use the "distr" button (first hit the blue "2nd" button, then "vars"). Then scroll down to "2:normalcdf"

For "lower:", type in 160

For "upper:", type in a very large number. I used 1E99 but any large number (like 1 million) will work.

For "μ:", type in 120

For "σ:", type in 16

Select "Paste" hit "Enter" then hit "Enter" a second time to get the answer 0.0062096799

To turn this into a percent, multiply it by 100 which results in 0.62%