Jims systolic blood pressure is a random variable with a mea

Jim\'s systolic blood pressure is a random variable with a mean of 140 mmHg and a standard deviation of 12 mmHg. For Jim\'s age group, 140 is the threshold for high blood pressure.

Assume the data given follows the normal probability distribution.

If Jim\'s systolic blood pressure is taken at a randomly chosen moment, what is the probability that it will be 130 or less?

If Jim\'s systolic blood pressure is taken at a randomly chosen moment, what is the probability that it will be 173 or more?

If Jim\'s systolic blood pressure is taken at a randomly chosen moment, what is the probability that it will be between 111 and 160? (

Solution

Normal Distribution
Mean ( u ) =140
Standard Deviation ( sd )=12
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X <= 130) = (130-140)/12
= -10/12= -0.8333
= P ( Z <-0.8333) From Standard Normal Table
= 0.2023

b)
P(X >= 173) = (173-140)/12
= 33/12 = 2.75
= P ( Z >2.75) From Standard Normal Table
= 0.003                  
To find P(a < = Z < = b) = F(b) - F(a)
c)
P(X < 111) = (111-140)/12
= -29/12 = -2.4167
= P ( Z <-2.4167) From Standard Normal Table
= 0.00783
P(X < 160) = (160-140)/12
= 20/12 = 1.6667
= P ( Z <1.6667) From Standard Normal Table
= 0.95221
P(111 < X < 160) = 0.95221-0.00783 = 0.9444