Porphyrin is a pigment in blood protoplasm and other body fluids that is signifi

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 adults, x is approximately normally distributed with mean 38 and standard deviation 12. What is the probability that

(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

Solution:

Given in the Question:

Mean =38

SD = 12

P(X<60)

Z = (60-38)/12 = 1.8333

From Z table P(X<60)= 0.9664 or 96.64%

For P(X>16)

Z = (16-38)/12 = -1.8333

From Z table P(X>16) = 1-0.0336 = 96.64%

Probability(16<X<60) = 1-2(0.0336)

P(16<X<60) = 0.9328 or 93.28%

Probability of X>60= 1-P(X<60) = 1- 0.9664 = 0.0336 or 3.36%

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