Question 4 (15 pts). A simple random sample of 100 households located in a city recorded the number of people living in the household, X. It is known that there are 10,000 households in the city. From the sample, we find that the sample mean X = 11 and the sample variance S? = 25. (a) Find a 95% confidence interval for the population mean using the normal approxi- mation of t distribution. (b) In the same survey, 80% of the (sampled) households have cable tv. Find a 95% and and 99% confidence interval for the proportion of households having cable tv