Let Y have the beta distribution with parameters and whose mean and variance are given in Section 3.1 of the text. Use S (in particular, the functions pbeta and qbeta) to investigate the following conjecture: if , then the distribution of is close to the standard normal distribution. How large do and have to be for the approximation to be accurate in the sense of (a) ? How large do and have to be so that the approximation is accurate in the sense of (b)?