In Exercises $5$ and $6,$ determine the minimum sufficient sample size.

$5.$ Use the point estimate for $$ from Exercise $1.$ Determine the minimum survey size that is necessary to be $95\%$ confident that the sample mean waking time is within $10$ minutes of the actual mean waking time.

$6.$ Now suppose you want $99\%$ confidence with a maximum error of $2$ minutes. How many people would it be necessary to survey? $=80\mathrm{.}64$