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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