During a recent drought, a water utility in a certain town sampled 100 residential water bills and found that 73 of the residences had reduced their water consumption over that of the previous year. a) Find a 95% confidence interval for the proportion of residences that reduced theirwater consumption. b) Find a 99% confidence interval for the proportion of residences that reduced their water consumption. c) Find the sample size needed for a 95% confidence interval to specify the proportion towithin ±0.05.d) Find the sample size needed for a 99% confidence interval to specify the proportion towithin ±0.05.e) Someone claims that more than 70% of residences reduced their water consumption. With what level of confidence can this statement be made?f) If 95% confidence intervals are computed for 200 towns, what is the probability thatmore than 192 of the confidence intervals cover the true proportions?