The actual proportion of families in a certain city who own $($rather than rent$)$ their home is p $=0\mathrm{.}70.$ Suppose $($n $=84$ families in this city are to be

surveyed at random and their responses to the question of whether they own their home are assumed to be independent.

Note that if we denote S$,=$ the number of "yes"$-$es in the survey, then S$,$ ~ Bin$($n; p$).$

Also denote f $=*=$ the proportion of "yes"$-$es in the survey

Part $($a$)$

What is the exact probability that the value we obtain for the sample proportion f $=$

Sn will be at most $0\mathrm{.}06$ away from the true proportion p $=0\mathrm{.}72$ In

n

other words, find the probability P$($lf $-$ p$|<0\mathrm{.}06)?$ Write your answer as R variable pexact, i$.$e$.$

pexact $=$

Do not round your answer.