Question

A World Health Organization study (the MONICA project) of health in various countries reported that in Canada, systolic blood pressure readings have a mean of 115 and a standard deviation of 13. A reading above 147 is considered to be high blood pressure.

(a) How many standard deviations away from the mean is a blood pressure reading of 147? z = (3 decimal places)

(b) If systolic blood pressure in Canada is approximately normal, find the proportion of Canadians that suffer from high blood pressure. (3 decimal places)

(c) If systolic blood pressure in Canada is approximately normal, what is the probability that a randomly selected Canadian has a systolic blood pressures in the range from 103 to 147. (3 decimal places)

Answer 1

We are given that and .  

(a). Given Blood pressure reading is 147. This is 147-115=32 points away from the mean. And hence times the SD 13. ie Z=2.462.

(b). It is given that a reading above 147 is high blood pressure. The proprtion of Canadians above 147 is

P(X>147). We know that will have a standard Normal distribution

When X=147,

ie the proportion of Canadians that suffer from high blood pressure.= 0.69%.

(c). The probability that a randomly selected Canadian has a systolic blood pressures in the range from 103 to 147

ie P(103<X<147),

When X=103,

P(103<X<147)=P(-0.923<Z<2.462)=P(Z<2.462)-P(Z<-0.923)

=0.9931-0.1780=0.8151

The probability that a randomly selected Canadian has a systolic blood pressures in the range from 103 to 147=0.8151.