Answer
18.69 and 25.71 are the quartiles
Work Step by Step
.25 and .75 have normal values of -.675 and .675, respectively.
$(x - 22.2)/5.2 = -.675$
$(x - 22.2) = -3.51$
$ x = 18.69$
$(x - 22.2)/5.2 = .675$
$(x - 22.2) = 3.51$
$ x = 25.71$