A product developer at a cosmetics company has developed a new shampoo especially for redheads. In order to know if it is worthwhile to launch the product in Tasmania, the marketing manager needs an estimate of the proportion of the Tasmanian population who are redheads. A random sample of 500 Tasmanians is taken, and this reveals that 32 are redheads. a) Determine a 95% confidence interval for the proportion of all Tasmanians who are redheads. [4 marks] b) If the marketing manager needs to be 99% confident of estimating the population proportion within an error of +/-1%, how many additional people need to be randomly sampled. [3 marks]