Question

The systolic blood pressure of adults in the USA is distributed with a mean of 121 and SD of 16.

Someone qualifies as having stage 2 high blood pressure if their systolic pressure is 160 or higher.

A. What percentage of adults in the USA have stage 2 high blood pressure?

B.Stage 1 BP is specified as systolic BP between 140 and 160. What percentage of adults have stage 1?

C. your doctor tells you that you are in the 30th percentile or bottom 30% for BP among US adults. What is your systolic BP?

Answer 1

It is given that the BP follows a Normal distribution with and . Let us call the BP as X.

A. What percentage of adults in the USA have stage 2 high blood pressure?

We know that if X~N(, follows a standard Normal variate.

When X=160, we get

Therefore P(X>160)=P(Z>2.4375)=0.0074

The percentage of adults in teh USA have stage high BP=0.74%

B.Stage 1 BP is specified as systolic BP between 140 and 160. What percentage of adults have stage 1.

This is P(140<X<160). When X=140,

  

=0.1101

Therefore, percentage of adults have stage 1=11.01%

C. your doctor tells you that you are in the 30th percentile or bottom 30% for BP among US adults. What is your systolic BP?

First let us first find that value of a such that

P(Z<-a)=0.3

This pint is a=-0.5244.

When Z=-0.5244,

.

Therefore, my Systolic BP is 113.