Use the Diamonds dataset on the second tab of the data file.

Big T Jewelers is a local jewelry shop that is thinking of getting into the retail diamond business. As part of their pricing strategy, they have obtained a dataset that lists the characteristics and retail sale prices of over 2,000 unset diamonds that were sold at retail in the area. You work for Foxy Consulting, which has been hired by Big T.Big T wants to know whether they can use the information in the dataset to help better understand the relationship between the attributes of a diamond and its price.

1. (6 points) Would it be reasonable to model Carat Weight using a normal distribution (i.e., use a normal probability model for the data)? Explain your rationale to your (analytically competent) manager. You want to impress her, so try to list multiple criteria, if possible, so that she is sure that you understand your reasoning.

1. (6 points) The cut of a diamond is judged by gemologists on a five level scale: Excellent, Very Good, Good, Fair, Poor.[1] In this dataset, is there a relationship between Cut and price? Using only techniques that we have covered so far in class, write a very short, managerial summary of your findings. You may include a well-formatted visualization if it aids managerial understanding.
2. Model the relationship between diamond size (measured in carat weight) and price.
   1. (10 points) Write a managerial summary of your findings that would be appropriate if you were writing to your client and your manager at Foxy Consulting. Note, your manager is an analytics expert, and she wants to make sure that the model is appropriate and that you understand its interpretation so that you can later present it to the client.
   2. (4 points) The client wants to understand what the average difference in eventual sales price would be between a 1.25 and a 1.5 ct diamond.Write an appropriate response.

[1] In practice, "poor" cut diamonds are not usually sold as gemstones.