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 μ = 41 and standard deviation σ = 9. 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.)

Answer 1

a) P[X<60]

=P[Z<2.11]

=0.9826....................by using normal probability table.

b) P[X>16]

=P[Z>-2.78]

=1-0.0027...............by using normal probability table.

=0.9973

c) P[16<X<60]

=P[-2.78<Z<2.11]

=0.9826-0.0027...............by using normal probability table.

=0.9799

d) P[X>60]

=P[Z>2.11]

=1-0.9826

=0.0174...............by using normal probability table.