A biologist is breeding fruit flies to include a specific genetic mutation that will be useful in understanding memory in humans. To check whether a fly has the mutation, a DNA sequence is analyzed in a way that kills the fly, so the biologist only wants to test a sample of the flies to estimate the proportion of flies that have the mutation. The biologist selects 40 flies to sequence at random and finds that 9 of them have the genetic mutation. 1. Based on this sample, estimate the proportion of flies in this group that has the genetic mutation. 2. The scientist is worried that only having one sample may not be reliable for estimating the proportion of flies with the mutation, but does not want to sacrifice more flies to get a larger sample. The proportion from the sample is a good estimate for the population proportion, but it is difficult to understand the possible variability from a single value. Andre has a suggestion for how to better understand the variability: a. Assume the sample is representative of the population of flies and create a simulation that mimics what the scientist found. Andre gets 200 pieces of paper and marks 45 of them as Mutant and puts them all in a bag. Since Andre decided to use 200 pieces of paper, why should 45 of them be marked Mutant? What are some other combinations of total number of pieces of paper and number marked Mutant that he could use?