Hoping to lure more shoppers downtown, a city builds a new public parking garage in the central business district. The city plans to pay for the structure by charging fees for parking. A random sample of 44 weekdays was collected from a time horizon of several years and daily fees collected averaged $126 with a standard deviation of $15.

1. Show that the conditions for constructing a confidence interval are met in this scenario. Show all worl.
2. Calculate and interpret a 95% confidence interval. Show all applicable formulas, substitutions, and work
3. A consultant predicted that the parking revenues would average $135 per day. Based on the confidence interval, do you think the consultant was correct? Explain.
4. After constructing your confidence interval, you decide that you are unsatisfied with the margin of error that he calculated and want to reduce the margin of error to $2.50. Assuming you still wants to maintain a 95% confidence interval, what sample size do you need to collect?