Answer to Question #344803 in Statistics and Probability for Josh

Question

If the systolic pressure for a certain group of obese people has mean of 132 and a standard deviation of 8, find the probability that a randomly selected person will have the following blood pressure. Assume the variable is normally distributed.

a. Above 130

b. Below 150

c. Between 125 - 158

Answer 1

a) $P(X>130)=P(Z>\frac{130-132}{8})=P(Z>-0.25)=1-P(Z<-0.25)=1-0.4013=0.5987$

b) $P(X<150)=P(Z<\frac{150-132}{8})=P(Z<2.25)=0.9878$

c) $P(125<X<158)=P(\frac{125-132}{8}<Z<\frac{158-132}{8})=P(-0.875<Z<3.25)=$

$=P(Z<3.25)-P(Z<-0.88)=0.9994-0.1894=0.81$

(We find P using z-score table)