Question

The concentration of the active ingredient in capsules of a prescription painkiller varies according to a normal distribution with u=10% and o=0.2%. A) What is the median concentration? Explain your answer. B) What interval of concentrations covers the middle 95% of all capsules? C) What interval covers the middle half of all capsules?

Answer 1

(a) Normal curves are symmetric, so median = mean = 10%.

(b) Because 95% of values lie within 2σ of μ, μ 2σ = 10 2(0.2) = 10 0.4 implies 9.6% to 10.4% is the range of concentrations the cover the middle 95% of all the capsules.

(c) The range between the two quartiles covers the middle half of all capsules. Thus, μ 0.67σ = 10 0.67(0.2) = 10 0.134 implies 9.866% to 10.134% is the desired range.