A random sample of 70 suspension helmets used by motorcycle riders and automobile race-car drivers was subjected to an impact test, and on 18 of these helmets, some damage was observed. Round the value of P to 4 decimal places for all intermediate calculations.

(a) Find a 95% two-sided confidence interval on the true proportion of helmets of this type that would show damage from this test. Round the answers to 3 decimal places.

(b) Using the point estimate of p obtained from the preliminary sample of 70 helmets, how many helmets must be tested to be 95% confident that the error in estimating the true value of p is less than 0.02?

(c) How large must the sample be if we wish to be at least 95% confident that the error in estimating p is less than 0.02, regardless of the true value of p?