An experimenter publishing in the Annals of Botanyinvestigatedwhetherthestem diameters of the dicot sunflower would change depending on whether the plant was left to sway freely in the wind or was artificially supported. Suppose that the unsupported stem diameters at the base of a particular species of sunflower plant have a normal distribution with an average diameter of 35 mm and a standard deviation of 3 mm.

Find the value x0 such that 97.5% of the sunflowers have smaller diameters?