Question

A health study reported​ that, in one​ country, systolic blood pressure readings have a mean of 119 and a standard deviation of 15 . A reading above 140 is considered to be high blood pressure. Complete parts a through d below.

a) What is the​z-score for a blood pressure reading of​130?

b) If systolic blood pressure in that country has a normal​ distribution, what proportion of the population suffers from high blood​ pressure?

c) What proportion of the population has systolic blood pressure in the range from 103 to 140?

Answer 1

Given

$\mu$ =119

$\sigma$ =15

when x=130

Z s core is given by

T 11 Z=

$Z=\frac{130-119 }{15 } = 0.7333$

The​ z-score for a blood pressure reading of​130 = 0.7333 Answer

systolic blood pressure is greater than 140 considerd as high blood pressure

now

Z = 140 – 119 15 = 1.4

P(X >140 ) = 1- area from left to( Z =1.4)

=1- 0.919243

= 0.080757

proportion of the population suffers from high blood​ pressure = 8.076% Answer

(c)

when x=103

$Z=\frac{103-119 }{15 } = -1.067$

P (blood pressure in the range from 103 to 140 ) = area from left to (z=1.4) - area from left to (z=-1.067)

= 0.919243 - 0.142986

= 0.776257

proportion of the population has systolic blood pressure in the range from 103 to 140 = 77.63% Answer