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 = 45 and standard deviation σ = 11. 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

Solutions:
Given that,
μ =45 , σ=11
a)
P(X< 60)= p{[(x- μ)/σ]<[(60- 45)/11]}
=P(z<1.36)
=0.9131 ( from Standard Normanl table)

b)P(X>16)=1-P(X<=16)
=1- p{[(x- μ)/σ]<=[(16- 45)/11]}
= 1- P(z<= -2.64)
=1-0.0041 ( from Standard Normanl table)
=0.9959
C)
P(16<X< 60)= p{[(16- 45)/11]<[(x- μ)/σ]<[(60- 45)/11]}
=P(-2.64<Z<1.36)
= p(Z<1.36) - p(Z< -2.64)
= 0.9131- 0.0041 ( from. Standard Normanl table)
=0.9090
D)
P(X>60)=1-P(X<=60)
=1- p{[(x- μ)/σ]<=[(60- 45)/11]}
= 1- P(z<= 1.36)
=1-0.9131 ( from Standard Normanl table)
=0.0869