Statistics Questions

Question

The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of 119 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.

 %

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!

 people

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?

 %

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.

 lbs

Answer 1

x = blood pressure mean 119 SD 16

use standardized normal variable: z = (x - mean)/SD = (x - 119)/16

a) P(x > 160) = P(z > (160-119/16)) = P(z > 2.56) = P(z < -2.56) = 0.0052 = 0.52%

b) 2000 * 0.0052 = 10.4 ~ 10 people

c) P(140 < x < 160) = P((140-119/16) < z < (160-119/16)) = P(1.31 < z < 2.56) = P(z < 2.56) - P(z < 1.31) = 0.9948 - 0.9049 = 0.0899 = 8.99%

d) find z-score for 30th percentile (probability = 0.30) = -1.88

z = (x - mean)/SD

where x is value for 30th percentile

-1.88 = (x - 119)/16

16 * -1.88 + 119 = 88.92