Question

The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of 117 and standard deviation of 19 .

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.

%

(b) Stage 1 high BP is specified as systolic BP between 140 and 160. What percentage of adults in the US qualify for stage 1? Give your answer rounded to two decimal places.

%

(c). Your doctor tells you you are in the 30th percentile (e.g. bottom 30%) for blood pressure among US adults. What is your systolic BP? Give your answer rounded to two decimal places.

lbs

Answer 1

The systolic blood pressure of adults in USA is normally distributed with mean 117 and standard deviation of 19.

So, if X be the random variable denoting the systolic blood pressure of a randomly selected adult in USA, then X follows normal with mean 117 and standard deviation 19.

So, we can say that

Z=(X-117)/19 follows standard normal with mean 0 and standard deviation 1.

Question a

someone qualifies as having stage 2 high blood pressure if systolic blood pressure is more than 160.

So, we have to find

So, the corresponding percentage is 0.012*100, ie. 1.2%.

So, 1.2% of USA adults should have stage 2 high blood pressure.

Question b

Stage 1 high blood pressure is between systolic blood pressure 140 and 160.

So, we have to find

So, the corresponding percentage is 0.101*100, ie. 10.1%.

So, 10.1% of USA adults have stage 1 high blood pressure.

Question c

We have to find the 30th percentile for the systolic blood pressure.

So, we have to find m, such that

P(X<m)=0.3

So,

Now, from the standard normal table, we find that

Comparing, we get that

So, the 30th percentile is 107.044.

So, my systolic blood pressure is 107.044.