Question

The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of 121 millimeters of mercury (mmHg) and standard deviation of 17.

Someone qualifies as having Stage 2 high blood pressure if their systolic blood pressure is 160 or higher. Stage 1 high BP is specified as systolic BP between 140 and 160.

Give your answers rounded to 4 decimal places.

a. What is the probability that an adult in the USA has stage 2 high blood pressure?


b. What is the probability that an adult in the USA has stage 1 high blood pressure?


c. Your doctor tells you you are in the 30th percentile for blood pressure among US adults. What is your systolic BP?
mmHg

d. What is the systolic blood pressure that cuts off the top 2.5% of adults in the USA?
mmHg

Answer 1

for normal distribution z score =(X-μ)/σ
here mean=       μ=	121
std deviation   =σ=	17.000

a)

probability =P(X>160)=P(Z>(160-121)/17)=P(Z>2.29)=1-P(Z<2.29)=1-0.989=0.0110

b)

probability =P(140<X<160)=P((140-121)/17)<Z<(160-121)/17)=P(1.12<Z<2.29)=0.989-0.8686=0.1204

c)

for 30th percentile critical value of z=		-0.520
therefore corresponding value=mean+z*std deviation=			112.16

d)

for 97.5th percentile critical value of z=		1.960
therefore corresponding value=mean+z*std deviation=			154.32