Porphyrin is a pigment in blood protoplasm and other body fluids that is signifi
ID: 3159189 • Letter: P
Question
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 = 36 and standard deviation = 15. 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.)
Explanation / Answer
a)For X=60, z=(x-mu)/sigma
=(60-36)/15=1.6
Thus, P(X<60)=P(z<1.6)=0.9452
b)For X=16, z=(x-mu)/sigma
=(16-36)/15=-1.33
Thus, P(X>16)=P(z>-1.33)=1-P(z<-1.33)=1-0.0918=0.9082
c)P(16<X<60)
=P(X<60)-P(X<16)=P(z<1.6)-P(z<-1.33)=0.9452-0.0918=0.8534
d)P(X>60)=1-P(x<60)=1-P(z<1.6)=1-0.9452=0.0548