Question

The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of 121 and standard deviation of 25 . Someone qualies 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) Stage 1 high BP is specied as systolic BP between 140 and 160. What percentage of adults in the US qualify for stage 1? Give your answer rounded to two decimal places. % (c). Your doctor tells you you are in the 30th percentile (e.g. bottom 30%) for blood pressure among US adults. What is your systolic BP? Give your answer rounded to two decimal places.

Answer 1

Solution :

Given that,

mean = = 121

standard deviation = = 25

a ) P (x > 160)

= 1 - P (x < 160 )

= 1 - P ( x -  / ) < ( 160 - 121 / 25)

= 1 - P ( z < 39 / 25 )

= 1 - P ( z <1.56 )

Using z table

= 1 - 0.9406

= 0.0594

Probability = 0.0594

b ) P (140 < x < 160 )

P ( 140 - 121 / 25) < ( x -  / ) < ( 160 - 121 / 25)

P ( 19 / 25 < z < 39 / 25)

P (0.76 < z < 1.56 )

P ( z < 1.56 ) - P ( z < 0.76)

Using z table

= 0.9406 - 0.7764

= 0.1642

Probability = 0.1642 = 16.42%

c ) P(Z < z) =30%

P(Z < z) = 0.30

P(Z < -0.524 ) = 0.30

z = - 0.52

Using z-score formula,

x = z * +

x = - 0.52 * 25 + 121

x = 107.90

The 30th percentile = 107.90