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 = 43 and standard deviation σ = 13. 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 that ,

mean = = 43

standard deviation = = 13

(a)

P(x < 60) = P[(x - ) / < (60 - 43) / 13]

= P(z < 1.31)

= 0.9049

(b)

P(x > 16) = 1 - P(x < 16)

= 1 - P[(x - ) / < (16 - 43) / 13]

= 1 - P(z < -2.08)

= 0.9812.

(c)

P(16 < x < 60) =

= P(60 < x < 16)

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

= 0.9049 - 0.0188

= 0.8861

(d)

P(x > 60) = 1 - P(x < 60)

= 1 - P[(x - ) / < (60 - 43) / 13]

= 1 - P(z < 1.31)

= 1 - 0.9049

= 0.0951