59. The concentration of the active ingredient in capsules of a prescription painkiller varies according to a normal distribution with and .
59.
(a) Normal curves are symmetric, so .
(b) Because 95% of values lie within of implies that 9.6% to 10.4% is the interval of concentrations that cover the middle 95% of all the capsules.
(c) The interval between the two quartiles covers the middle half of all capsules. Thus, implies that 9.866% to 10.134% is the desired range.