A childrens clothing manufacturer is assessing how appropriate their sizing is for the children living in a particular area. They have collected information on the heights of a large sample of 6-year-old children from the area. They wish to ensure that their age 6 clothing will fit or be too big for 80% of the 6-year-old children (fit being determined using the height of each child).

a) Which of the distributions covered in the module would be the best choice to calculate size of clothing required? How should they get the appropriate parameters for their calculations? Explain the reasons for your selection.

b) What assumptions would you be making in modelling with the method given in part a)? How realistic are these assumptions?