About 11% of Americans believe that Joan of Arc was Noah’s wife. (Source: Harper’s Index, Volume 3.) At a large freshman symposium, a college professor (jokingly) says that Joan of Arc was Noah’s wife. Assume that college freshmen are representative of the general American population regarding biblical knowledge.
(a) If the symposium was attended by 55 freshmen, what is the probability that up to 15% of the freshmen believe the professor’s claim?
(b) What is the probability that between 10% and 15% (including 10% and 15%) of the freshmen believe the professor’s claim? 

(c) Is the normal approximation to the proportion p̂ = r/n valid in this application? Explain.