Question

Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Assume porphyrin is normally distributed with mean (mu) = 38 milligrams per deciliter and standard deviation (sigma) = 12 milligrams per deciliter.

a) What is the probability that x is less than 56?

b) What is the probability that x is greater than 23?

c) What is the probability that x is between 23 and 56?

Answer 1

Given: = 38 and σ= 12 a)When,X-56 z= -= 1.5 p(x< 56)=p(ž< 1.5 )-| 0.9332| By standard normal table b)When,x: 23 Z1.25 Therefore p(x> 23 )=p (z >-1.25 ) p(z < 1.25 )=10.8944 |By standard normal table =

c)When,x-23 x-μ -1.25 -1.25 z_-= p(x23) -p(z < -1.25)-0.1056 By standard normal table (negative values) When,x- 56 Z1.5 Therefore p(x< 56,-pC< 1.5 )=| 0.9332|By standard normal table The required probability is p( 23< x< 56) p(-1.25 <z< 1.5 ) =p(z < 1.5 )-p(2<-125) 0.9332 - 0.1056 0.8275