A random sample of 60 suspension helmets used by motorcycle riders and automobile race-car drivers was subjected to an impact test, and some damage was observed on 22 of these helmets. (a) Find a 99% two-sided confidence interval on the true proportion of helmets that would show damage from this test. (b) Using the point estimate of p from 60 helmets, how many helmets must be tested to be 99% confident that the error in estimating p is less than 0.015? (c) How large must the sample be if we wish to be at least 99% confident that the error in estimating p is less than 0.02 regardless of the true value of p?