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1. A personal nance company wants to estimate the gross income of its clients. From previous data, it knows incomes have a standard deviation of 16000. It conducts a survey which it sends out to all its customers and gets back 56 responses (34% response rate), which give an average income of 63000. (a) What distribution do you think is the best to use to model the sample mean in this case, and why? What will the standard deviation of the sample mean be? (b) Construct a 95% confidence interval for mean gross income. (c) Without doing any further calculations, state whether a 90% condence interval would be wider or narrower. Explain your answer. (d) Why might your sample be biased in this case? What effect might any bias have on your result in (b)