question archive The monthly income of each of the 500 service microenterprises in a city is a random variable with unknown mean μ

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The monthly income of each of the 500 service microenterprises in a city is a random variable with unknown mean μ. In order to simplify tax collection, the SRI has arranged that these companies be taxed monthly with 10% of their income From a random sample of 50 micro-companies, an average monthly income of $ 1000 was obtained with a standard deviation of $ 80.

a. Estimate the mean amount of income of the city's microenterprises with a 95% confidence interval

b. Estimate the average amount of collection for these microenterprises with a 95% confidence interval

c. If the purpose of the SRI is to achieve a total monthly collection of at least $ 52,000 to these microenterprises, is it feasible that its goals are met?

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