1. Collette is self-employed, selling items at Home Interior parties. She wants to estimate the average amount a client spends at each party. A random sample of 35 clients' receipts gave a sample mean of $34.70 and historically we know the population standard deviation of spending at these parties to be $4.85.

1. (1 point) Explain why you may assume your data is normally distributed.

1. (1 point) Find a 90% confidence interval for the average amount any given client can be expected to spend at a party.

1. (1 point) Write an brief explanation of the meaning of the confidence interval in the context of this problem

1. (1 point) For a party with 35 clients, use part (b) to estimate a range of dollar values for Collette's total sales at that party.

T-Distribution Intervals

2.(1 point) Confidence intervals are designed to predict where the population mean will fall. We use the Z distribution when we know the population standard deviation, and we use the T distribution when we have or can find the sample standard deviation. Explain why two different distributions are needed for this process?