2. An article in the October 11, 2006, issue of the Washington Post claimed that 15% of high school students used cursive writing on the essay portion of the SAT exam in the academic year 2005-2006 (Pressler). Suppose you take a random sample from these exams and see what proportion of the sample used cursive writing for the essay.

a. Report an expression for the standard deviation of the sample proportion, in terms of the sample size n.

NOTE: We don't know n, so n will be in your expression.

b. Use the empirical rule (68-95-99.7 rule) to determine how large the sample size would have to be for 95% of the sample proportions to fall between 0.10 and 0.20. Note: the first thing you want to do is figure out what the standard deviation is given this information. Then, set that standard deviation equal to the expression you found in part a) to solve for n.