The systolic blood pressure of adults in the USA is nearly normally distributed
ID: 3248923 • Letter: T
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. If you sampled 2000 people, how many would you expect to have BP> 160? Give your answer to the nearest person. Note: I had a bit of an issue encoding rounded answers, so try rounding both up and down if there's an issue!
c. Stage 1 high BP is specified as systolic BP between 140 and 160. What percentage of adults in the US qualify for stage 1? Round to 2 decimal places
d. Your doctor tells you you are in the 30th percentile for blood pressure among US adults. What is your systolic BP? Round to 2 decimal places.
Explanation / Answer
Answer:
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.
Z value for 160, z =(160-117)/19 =2.26
P( x >160) = P( z >2.26) =0.0119
The required percentage =1.19%
b. If you sampled 2000 people, how many would you expect to have BP> 160? Give your answer to the nearest person. Note: I had a bit of an issue encoding rounded answers, so try rounding both up and down if there's an issue!
2000*0.0119 =23.8
rounding up =24 (and rounding down =23)
c. Stage 1 high BP is specified as systolic BP between 140 and 160. What percentage of adults in the US qualify for stage 1? Round to 2 decimal places
Z value for 140, z =(140-117)/19 =1.21
P(140,x<16))= P( 1.21<z<2.26)= P( z<2.26)- P( z < 1.21)
=0.9881 -0.8869
=0.1012
The required percentage =10.12%
d. Your doctor tells you you are in the 30th percentile for blood pressure among US adults. What is your systolic BP? Round to 2 decimal places.
Z value for 30th percentile = -0.524
X=117-0.524*19 =107.044
my systolic BP=107.04.