Question

The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of 118 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) Stage 1 high BP is specified 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.

lbs

Answer 1

Solution :

Given that ,

mean = = 118

standard deviation = = 20

P(x > 160 ) = 1 - P( x< 160)

= 1- P[(x - ) / < ( 106 - 118) / 20 ]

= 1- P(z < 2.1)

Using z table,

= 1 - 0.9821

= 0.0179

= 01.79%

Answer = 01.79%

( b )

P( 140 < x < 160)

= P[( 140 - 118 ) / 20 ) < (x - ) /  < ( 160 - 118 ) / 20) ]

= P( 1.1 < z < 2.1)

= P(z < 2.1 ) - P(z < 1.1 )

Using z table,

= 0.9821 - 0.8643

= 0.1178

= 11.78%

Answer = 11.78%

( c )

The z - distribution of the 30% is

P(Z < z) = 30%

= P(Z < z ) = 0.30

= P(Z < -0.524 ) = 0.30

z = -0.524

Using z-score formula,

x = z * +

x = -0.524 * 20 + 118

x = 107.52

Answer = x = 107.52 lbs