Use the result of part (c) of Exercise 8.58 to set up an equation in n whose solution will give the sample size that is required to be able to assert with probability 1 – a that the proportion of the population contained between the smallest and largest sample values is at least p. Show that for ρ = 0.90 and α = 0.05 this equation can be written as (0.90)^n–1 = 1 / 2n+ 18 This kind of equation is difficult to solve, but it can be shown that an approximate solution for n is given by

1/2 + 1/4 ∙ 1 + p / 1 – p ∙ x²_α,4 where x²_α,4 must be looked up in Table V. Use this method to find an approximate solution of the equation for ρ = 0.90 and α = 0.05.