6.25 Sunflowers An experimenter publishing in the Annals of Botany investigated whether the stem diam- eters 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 millimetres (mm) and a standard deviation of 3 mm.

a. What is the probability that a sunflower plant will have a stem diameter of more than 40 mm?

b. If two sunflower plants are randomly selected, what is the probability that both plants will have a stem diameter of more than 40 mm?c. Within what limits would you expect the stem diameters to lie, with probability 0.95?

d. What diameter represents the 90th percentile of the distribution of diameters?