The New York Times is well known for its daily crossword puzzle, but they have another game that has become very popular: Spelling Bee. The goal is to make as many words as possible using the seven letters provided. If you find enough words, you can earn the title of "Genius".

For a particular day, you are interested in estimating the proportion of all Spelling Bee players that reached "Genius" status. Suppose you take a random sample of 50 Spelling Bee players for that day and find that 13 of them reached "Genius" status. Create a 95% confidence interval to estimate the population proportion of Spelling Bee players that reach "Genius" status.

1. You may assume the sample of Spelling Bee players is a random sample. Check the remaining necessary assumptions.
2. Compute the 95% confidence interval - show all work.
3. Provide an interpretation of the 95% confidence level (include context).

Please show all supporting work and clearly label your work for parts 1, 2, and 3.