Assuming a normal distribution of Blood pressure of a mean o

Assuming a normal distribution of Blood pressure of a mean of 120 with standard deviation of 10, what person would be considered to be unusual ? Using the statistical definition of \"unusual\", what % of the population would this be ??

Solution

let X be a random variable which follows normal distribution with mean mu and standard deviation sigma.

then the interval [mu-3sigma,mu+3sigma] is called the effective range. the value of X is more likely to fall within this range. so if X is out of this range then that is treated as \"unusual\" meaning that it is due to some other factors.

so in this case mu=120 and sigma=10

so the effective range is [120-30,120+30]=[90,150]

so a person would be treated as unusual if his Blood pressure is not in the range [90,150] that is if his blood pressure is below 90 or above 150.

so we have P[90<X<150]=P[(90-120)/10<(X-120)/10<(150-120)/0]=P[-3<Z<3]=0.9973   where Z~N(0,1)

so the % of population would be unusual is

100*[1-P[90<X<150]]=0.27% [answer]