A random sample of $50$ suspension helmets used by motorcycle riders and automobile race$-$car drivers was subjected to an impact test, and on $22$ of these helmets some damage was observed.

Find a $99\%$ two$-$sided confidence interval on the true proportion of helmets of this type that would show damage from this test.

Using the point estimate of p obtained from the preliminary sample of $50$ helmets, how many helmets must be tested to be $95\%$ confident that the error in estimating the true value of p is less than $0\mathrm{.}02?$