The National Patent Development Corporation (NPD) is a company that takes newly patented products from the design stage through consumer sales. In 1986, NPD acquired a new product that can be used to replace a dentist's drill. The product, called Caridex, is a solution that dissolves decayed matter in dental cavities without requiring drilling. After some research, it was discovered that Caridex works well only on cavities on the top surface of teeth, where a small fraction of cavities occur. It is known that 100,000 dentists in the United States treat cavities. A preliminary analysis revealed that only 10% of all dentists would use Caridex in the first year after its introduction. The dispensing unit costs NPD $200, and it intends to sell the unit at cost price. The solution costs NPD $0.50 per cavity and will be sold to dentists at a price of $2.50 per cavity. Fixed annual costs are expected to be $4 million. NPD would like an estimate of the profit it can expect in the first year of operation. Because NPD profits will depend completely on the number of cavities treated with Caridex during the year, NPD commissioned a survey of 400 dentists who planned to use Caridex. Each dentist was asked how many cavities he or she anticipates treating with Caridex during an average week.

(Note: The data is in the 'Project1_Data' file and is located on the 'Cavities' tab)'

You have time traveled back to 1986. You are free to assume that you brought the newest version of Excel with you. Your task, as the manager responsible for Caridex at NPD, is to determine:

a) Develop a 95% confidence interval for the first-year profits from Caridex. Discuss in detail all the steps you took. Clearly show all Excel output and discuss assumptions that you made. (39 points)

b) Based on your results in part a, determine if you can conclude from the survey that Caridex will make a profit in its first year. Clearly explain your thought process. (5 pts)

From the Data in the data file I found that:

Mean	4.015
Standard Error	0.088212
Median	4
Mode	4
Standard Deviation	1.764244
Sample Variance	3.112556
Kurtosis	0.415938
Skewness	0.662414
Range	9
Minimum	1
Maximum	10
Sum	1606
Count	400