An investor wants to decide whether it is a good investment to build a fitness centre with an aquatic sports facility in a Melbourne suburb. His main concern is the level of the total household annual income of the 4108 houses in the suburb. He commissioned a statistical consulting group to take a random sample of 35 households and the consulting group obtained an average household annual income of $175,000 and a sample standard deviation of $10,300.

1. Construct a 99% confidence interval estimate for the true average household annual income of the households in the suburb and provide a plain language interpretation of the interval. Show your workings.
2. Explain the assumptions that are necessary for the above confidence interval to be valid.