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 = 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

Solution :

Given that ,

a ) mean = = 43

standard deviation = = 11

P(x < 60 ) = P[(x - ) / < (60-43) / 11]

= P(z < 1.55)

probability = 0.9394

b )

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

= 1 - P[(x - ) / < (16-43) /11 ]

= 1 - P(z < -2.45 )

= 1 - 0.0071 = 0.9929.

probability = 0.9929

c )

P(16 < x <60 ) = P[(16-43)/11 ) < (x - ) /  < (60-43) /11 ) ]

= P(-2.45 < z <1.55 )

= P(z < 1.55) - P(z < -2.45 )

= 0.9394 - 0.0071 = 0.9323

probability = 0.9323

d)

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

= 1 - P[(x - ) / < (60-43) /11 ]

= 1 - P(z < 1.55 )

= 1 - 0.9394 =0.0606

probability = 0.0606