De steekproefproportie is \(\hat{p}={46 \over 210}=0{,}219...\)

\(\sigma =\sqrt{{\hat{p}(1-\hat{p}) \over n}}=\sqrt{{0{,}219...⋅0{,}780... \over 210}}=0{,}028...\)

\(\hat{p}-2\sigma =0{,}219...-2⋅0{,}028...≈0{,}162\text{.}\)

\(\hat{p}+2\sigma =0{,}219...+2⋅0{,}028...≈0{,}276\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval is \([0{,}162; 0{,}276]\text{.}\)

De steekproefproportie is \(\hat{p}=17\%=0{,}17\text{.}\)

\(\sigma =\sqrt{{\hat{p}(1-\hat{p}) \over n}}=\sqrt{{0{,}17⋅0{,}83 \over 103}}=0{,}0370...\)

\(\hat{p}-2\sigma =0{,}17-2⋅0{,}0370...≈0{,}096\text{.}\)

\(\hat{p}+2\sigma =0{,}17+2⋅0{,}0370...≈0{,}244\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval is \([9{,}6\%; 24{,}4\%]\text{.}\)

\(\bar{X}-2⋅{S \over \sqrt{n}}=925-2⋅{97 \over \sqrt{245}}≈913\text{.}\)

\(\bar{X}+2⋅{S \over \sqrt{n}}=925+2⋅{97 \over \sqrt{245}}≈937\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval voor het populatiegemiddelde is \([913, 937]\text{.}\)

\(\hat{p}={0{,}216+0{,}344 \over 2}=0{,}28\) en \(\text{breedte}=0{,}344-0{,}216=0{,}128\text{.}\)

Los op \(4⋅\sqrt{{0{,}28⋅0{,}72 \over n}}=0{,}128\text{.}\)

Voer in
\(y_1=4⋅\sqrt{{0{,}28⋅0{,}72 \over x}}\)
\(y_2=0{,}128\)
Optie 'intersect' geeft \(x=196{,}875\)

De steekproefomvang is dus \(197\text{.}\)

\(S=108\) en \(\text{breedte}=393-357=36\text{.}\)

Los op \(4⋅{108 \over \sqrt{n}}=36\text{.}\)

Voer in
\(y_1=4⋅{108 \over \sqrt{x}}\)
\(y_2=36\)
Optie 'intersect' geeft \(x=144\)

De steekproefomvang is dus \(144\text{.}\)