A real estate office wants to make a survey in a certain town, which has 50,000 households, to determine how far the head of households has to commute to work. A simple random sample of 1,000 households is chosen, the occupants are interviewed, and it is found that on average, the heads of the sample households commuted 8.7 miles to work; the SD of the distances was 9.0 miles. (All distances are one-way; if someone isn't working, the commute distance is defined to be 0.) a) The average commute distance of all 50,000 heads of households in the town is estimated as , and this estimate is likely to be off by or so.
b) If possible, find a 95%-confidence interval for the average commute distance of all heads of households in the town. If this isn't possible, explain why not.