Medical records at a doctor's office reveal that 12% of adult patients have seasonal allergies. Select a random sample of 100 adult patients and let Y = the number of individuals in the sample who have allergies.

(a) Calculate the mean and standard deviation of the sampling distribution of Y.

(b) Check the large Counts Condition.

(c) Find the probability that less than 7 patients have seasonal allergies.

(d) Would it be surprising to have 7 or fewer patients from the sample to have seasonal allergies?