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 = 45 and standard deviation σ = 14. 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 = = 45

standard deviation = = 14

a)

P(x < 60) = P((x - ) / < (60 - 45) / 14)

= P(z < 1.07)

= 0.8577 Using standard normal table,

Probability = 0.8577

b)

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

= 1 - P((x - ) / < (16 - 45) / 14)

= 1 - P(z < -2.07)

= 1 - 0.0192 Using standard normal table.

= 0.9808

Probability = 0.9808

c)

P(16 < x < 60) = P((16 - 45)/ 14) < (x - ) /  < (60 - 45) / 14) )

= P(-2.07 < z < 1.07)

= P(z < 1.07) - P(z < -2.07)

= 0.8577 - 0.0192

= 0.8385

Probability = 0.8385

d)

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

= 1 - P((x - ) / < (60 - 45) / 14)

= 1 - P(z < 1.07)

= 1 - 0.8577 Using standard normal table.

= 0.1423

Probability = 0.1423