Answer to Question #140973 in Statistics and Probability for Ally

Question

If the systolic blood pressure for a certain group of obese people has a mean of 135 and a standard deviation of 8, find the probability that a randomly selected person will have the following blood pressure: a. Above 152 b. Below 138 c. Between 128 and 167

Answer 1

a) $P(X>152)=P(Z>\frac{152-135}{8})=P(Z>2.13)=1-P(Z<2.13)=0.0166.$

b) $P(X<138)=P(Z<\frac{138-135}{8})=P(Z<0.38)=0.6480.$

c) $P(128<X<167)=P(\frac{128-135}{8}<Z<\frac{167-135}{8})=P(-0.88<Z<4)=$

$=P(Z<4)-P(Z<-0.88)=0.8106.$