Porphyrin is a pigment in blood protoplasm and other body fluids that is signifi
ID: 3154634 • 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 = 41 and standard deviation = 14. 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=(60-41)/14=1.35
P(X<60)=P(z<1.35)=0.9115
(b)For X=16, z=(16-41)/14=-1.78
P(X>16)=1-P(X<16)=1-P(z<-1.78)=1-0.0375=0.9625
(c)P(16<X<60)
=P(X<60)-P(X<16)
=P(z<1.35)-P(z<-1.78)
=0.9115-0.0375
=0.874