One of the reasons why customers prefer to stay in Airbnb is because of its low cost. It is claimed that the average price for a Private room type of Airbnb in Sydney could be as low as $65 per night. A sample of 400 Private room type of Airbnb Sydney gave a mean price of $114 per night with a standard deviation of $520.

You are asked to see if the claim can be supported by constructing a 95% confidence interval of the population average price of all Private room type of Airbnb Sydney. Write inerval up to 3dp and explain why or why not the claim can be supported. In addition, check whether the assumption is satisfied.