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 = 44 and standard deviation σ = 10. 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 = = 44

standard deviation = =10

a ) P( x < 60 )

P ( x - / ) < ( 60 - 44 / 10)

P ( z < 16 / 10 )

P ( z < 1.6)

Using z table

= 0.9452

Probability = 0.9452

b ) P (x > 16 )

= 1 - P (x < 16 )

= 1 - P ( x -  / ) < ( 16 - 44 / 10)

= 1 - P ( z <- 28 / 10 )

= 1 - P ( z < -2.8)

Using z table

= 1 - 0.0026

= 0.9974

Probability = 0.9974

c) P (16 < x < 60 )

P ( 16 - 44 / 10) < ( x -  / ) < ( 60 - 44 / 10)

P ( - 28 / 10 < z < 16/ 10 )

P (-2.8 < z < 1.6)

P ( z < 1.6 ) - P ( z <-2.8)

Using z table

= 0.9452 - 0.0026

= 0.9426

Probability = 0.9426

d) P (x > 60 )

= 1 - P (x < 60 )

= 1 - P ( x -  / ) < ( 60 - 44 / 10)

= 1 - P ( z < 16 / 10 )

= 1 - P ( z < 1.6)

Using z table

= 1 - 0.9452

= 0.0548

Probability = 0.0548