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 = 37 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

Given,

= 37 , = 11

We convert this to standard normal as

P(X < x) = P( Z < x - / )

a)

P( X < 60) = P( Z < 60 - 37 / 11)

= P( Z < 2.0909)

= 0.9817

b)

P( X > 16) = P( Z > 16 - 37 / 11)

= P( Z > -1.9091)  

= P( Z < 1.9091)

= 0.9719

c)

P( 16 < X < 60) = P( X < 60) - P( X < 16)

= P( Z < 60 - 37 / 11) - P( Z < 16 - 37 / 11)

= P( Z < 2.0909) - P( Z < -1.9091)

= 0.9817 - 0.0281

= 0.9536

d)

P( X > 60) = P( Z > 60 - 37 / 11)

= P( Z > 2.0909)

= 0.0183