Porphyrin is a pigment in blood protoplasm and other body fluids that is signifi
ID: 3319851 • 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 = 39 and standard deviation = 10. 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
Mean is 39 and s is 10
z is given as (x-mean)/s
a) P(x<60)=P(z<(60-39)/10)=P(z<2.1), from normal distribution table we get 0.9821
b) P(x>16)=P(z>(16-39)/10)=P(z>-2.3) or P(z<2.3) =0.9893
c) P(16<x<60)=P((16-39)/10<z<(60-39)/10)=P(-2.3<z<2.1)=P(z<2.1)-(1-P(z<2.3))=0.9821-(1-0.9893)=0.9714
d) P(x>60)=1-0.9821=0.0179