Your investment advisor proposes a monthly income investment scheme which promises a variable income each month. You will invest in it only if you are assured an average monthly income of at least 500 dollars. Your advisor also tells you that, for the past 51 months, the scheme had incomes with an average value of 510 dollars and a standard deviation of 108 dollars. (a) Create a 99% confidence interval for the average monthly income of this scheme. (Round your answers to 4 decimal places, if needed.)

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