Question

Polychlorinated biphenyls (PCBs) are a class of environmental chemicals associated with a variety of adverse health effects and which can also be found in human fat. Researchers analysed PCB concentrations in the fat of a group of adults and found that the concentrations followed a Normal distribution with a mean of 1600 ng/g lipid weight. Supposing they reported that a value of 2468 ng/g lipid weight would put an adult in the top 10% of PCB concentrations, the standard deviation of the distribution must have been at most....

Answer 1

Given that,

mean = = 1600

standard deviation = =2468

Using standard normal table,

P(Z > z) =10 %

= 1 - P(Z < z) = 0.10

= P(Z < z ) = 1 - 0.10

= P(Z < z ) = 0.90

= P(Z < 1.28 ) = 0.90  

z = 1.28 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= 1.28*2468+1600

x= 4759.04

x=4759