A market research group takes a random sample of eight of a city's fifty precincts. Every household in each sampled precinct is questioned as to whether it has a central air-condi tioning system and also on its summer monthly electricity costs. The results are shown in the table. MEAN MONTHLY SAMPLED PRECINCT NUMBER OF HOUSEHOLDS ELECTRICITY COSTS (5) NUMBER WITH CENTRAL AIR CONDITIONING 89359958 84 43 64 29 22 24 49 37 68 30 59 13 25 77 21 42 14 63

(a) Find a 95% confidence interval for the population mean summer monthly electricity costs.

(b) Find a 95% confidence interval for the population proportion of households with cen- tral air conditioning.