A company produces 1,000 blue crayons every day. A sample of 50 crayons are analyzed, and 3 of them are found to not meet the standards of the company, so they are labeled defective. A simulation is run in which 50 crayons are chosen out of 1,000 so that each crayon chosen has a 6% chance of being defective. The simulation is run 500 times, and the mean proportion of defective crayons is 0.059 with a standard deviation of 0.012. What is a good margin of error based on this simulation? Based on a population proportion estimate and margin of error, is 0.07 a plausible value for the population proportion of crayons that are defective? Explain your reasoning.

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