Porphyrin is a pigment in blood protoplasm and other body fl

Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles, x is approximately normally distributed with mean = 39 and standard deviation = 13. Find the following probabilities. (Round your answers to four decimal places.)

(a) x is less than 60

(b) x is greater than 16


(c) x is between 16 and 60


(d) x is more than 60 (This may indicate an infection, anemia, or another type of illness.)

Solution

Normal Distribution
Mean ( u ) =39
Standard Deviation ( sd )=13
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X < 60) = (60-39)/13
= 21/13= 1.6154
= P ( Z <1.6154) From Standard Normal Table
= 0.9469                  
b)
P(X > 16) = (16-39)/13
= -23/13 = -1.7692
= P ( Z >-1.769) From Standard Normal Table
= 0.9616                  
c)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 16) = (16-39)/13
= -23/13 = -1.7692
= P ( Z <-1.7692) From Standard Normal Table
= 0.03843
P(X < 60) = (60-39)/13
= 21/13 = 1.6154
= P ( Z <1.6154) From Standard Normal Table
= 0.94689
P(16 < X < 60) = 0.94689-0.03843 = 0.9085