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 ? = 35 and standard deviation ? = 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 ,

mean = = 35

standard deviation = = 11

(a)

P(x < 60) = P((x - ) / < (60 - 35) / 11) = P(z < 2.27)

Using standard normal table,

P(x < 60) = 0.9884

Probability = 0.9884

(b)

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

= 1 - P((x - ) / < (16 - 35) / 11)

= 1 - P(z < -1.72)

= 1 - 0.0427   

= 0.9573

P(x > 16) = 0.9573

Probability = 0.9573

(c)

P(16 < x < 60) = P((16 - 35/ 11) < (x - ) / < (60 - 35) / 11) )

P(16 < x < 60) = P(-1.72 < z < 2.27)

P(16 < x < 60) = P(z < 2.27) - P(z < -1.72)

P(16 < x < 60) = 0.9884 - 0.0427

Probability = 0.9457

(d)

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

= 1 - 0.9884

= 0.0116   

P(x > 60) = 0.0116

Probability = 0.0116