Question

The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of 121 and standard deviation of 20 . 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.

Answer 1

Mean, = 121

Standard deviation, = 20

Corresponding to 160, the z value = (160 - 121)/20 = 1.95

(a) The percentage of adults in the USA having stage 2 high blood pressure = P(X ≥ 160) = P(Z ≥ 1.95)

= 2.56%

(b) Expected number of person with BP > 160 in 2000 people

= 0.0256*2000 = 51.2 ≈ 51

(c) Percentage of adults in the US who qualify for Stage 1 high BP = P(140 ≤ X ≤ 160)*100%

= P{(140 - 121)/20 ≤ Z ≤ (160 - 121)/20}

= P(0.95 ≤ Z ≤ 1.95) = 14.55%

(d)

Corresponding to 30th percentile, the Z score = -0.5245

Thus, the required systolic BP = (121 - 0.5245*20) = 110.51