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 = 36 and standard deviation σ = 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.)

Answer 1

Solution:

Given: X = the number of milligrams of porphyrin per deciliter of blood is approximately normally distributed with mean μ = 36 and standard deviation σ = 10

Part a) Find:

P( X < 60) = ...........?

Find z score for x = 60

thus

Look in z table for z = 2.4 and 0.00 and find corresponding area.

P( Z< 2.40) = 0.9918

thus

Part b) Find:

P( X > 16) = ..........?

Find z score for x = 16

thus

Look in z table for z = -2.0 and 0.00 and find corresponding area.

P( Z< -2.00 )= 0.0228

thus

Part c) Find:

from part a and b) we have for x = 16, z = -2.00 and for x = 60, z = 2.40

thus

Part d) Find:

P( X > 60) =.........?

From part a) for x = 60 , z = 2.40

thus

From part a) We have  P( Z< 2.40) = 0.9918

thus