Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 21 students, she finds 3 who eat cauliflower. Obtain and interpret a 95% confidence interval for the proportion of students who eat cauliflower on Jane's campus using Agresti and Coull's method.

Over the course of the school year, you keep track of how much snow falls on a given day and whether it was a snow day. your data indicates that of twenty-one days with less than three inches of snow, five were snow days, while of the eight days with more than three inches of snow, six were snow days. if all you know about a day is that it is snowing, what is the probability that it will be a snow day?