Question 4. (8 points) Assume that a population of newly discovered small creatures called "porgs" in a remote island lay eggs with three distinct appearances: patterned with dots, white, or dark grey. Last year, the porgs laid 30 dotted eggs, 13 were grey and 2 were white. Based on this information, please answer these questions.

A) (2.5 Points) What is the probability that you would only collect 2 white eggs?

B) (3 points) Construct a 90% confidence interval for the observed proportion of white eggs. Provide a one-sentence interpretation of this confidence interval.

C) (2.5 points) If you wanted the confidence interval in (B) to only be 4 percentages points wide (i.e, extending 2 percentage points on either side of the sample proportion), how many eggs would you need to collect?

Please answer the following questions and use a step by step process using the correct formulas if needed. Also please explain the answers. Thank you