5. 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 household has to commute to work. A simple random sample of 1,000 households is chosen. 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. (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 50. (b) If it's appropriate to do so, find a 95%confidence interval for the average commute distance of all heads of households in the town. If it is not appropriate, explain why not. 6. A simple random sample of 900 households is taken in a city. The average household size in the sample is 2.2 people, with an SD of 2 people. (a) For each part, circle the best answer. The average household size in the sample is (i) known to be 2.2 (ii) estimated to be 2.2 The average household size in the city is (i) known to be 2.2 (ii) estimated to be 2.2 (b) Is the histogram of household sizes in the sample is approximately normal? Why or why not? (c) What about the distribution of household sizes in the city? Do you think it is approximately normal? Why or why not? (d) TRUE or FALSE: There is a 95% chance that the average household size in the population is between 2.07 and 2.33 people