Question

Arsenic is a compound that occurs naturally in very low concentrations. Arsenic blood concentrations in healthy adults are Normally distributed, with mean ????=3.2μ=3.2 micrograms per deciliter (????g/dl)(μg/dl) and standard deviation ????=1.5 ????g/dlσ=1.5 μg/dl . What is the range of arsenic blood concentrations corresponding to the middle 90% of healthy adults?

Answer 1

range of arsenic blood concentrations: 0.725 μg/dl - 5.675 μg/dl

Explanation:

Data

μ=3.2 μg/dl

σ=1.5 μg/dl

Let's call x1 the maximum arsenic blood concentrations and x2 the minimum concentration for the range corresponding to the middle 90% of healthy adults. To get x1 is necessary to find the x for that the area below the standard normal distribution is 0.45. In table attached it can be seen that this area correspond to Z = 1.65. Using Z definition, x1 can be isolated

Z = (x1-μ)/σ = 1.65

x1 = 1.65*σ + μ

x1 = 1.65*1.5 + 3.2

x1 = 5.675 μg/dl

Knowing that normal distribution is symmetrical respect to 0, then the area between Z = -1.65 and Z = 0 is also 0.45. So, x2 is computed as

Z = (x2-μ)/σ = -1.65

x2 = -1.65*σ + μ

x2 = -1.65*1.5 + 3.2

x2 = 0.725 μg/dl