Assume that a population of newly discovered small creatures called "porgs" in a remote island lays eggs with three distinct appearances: patterned with dots, white, or dark grey. Last year, the porgs laid 35 dotted eggs, 30 grey eggs, and 20 white eggs. You randomly selected 25 eggs, 14 of which were dotted, 7 were grey and 4 were white. Based on this information, please answer these questions,

a. What is the probability that you would only collect 4 white eggs?

b. Construct a 90% confidence interval for the observed proportion of white eggs. Provide a one-sentence interpretation of this confidence interval.

c) If you wanted the confidence interval in (b) to only be 5 percentage points wide (i.e., extending 2.5 percentage points on either side of the sample proportion), how many eggs would you need to collect?