\(\bar{X}-2⋅{S \over \sqrt{n}}=341-2⋅{24 \over \sqrt{156}}≈337\text{.}\)

\(\bar{X}+2⋅{S \over \sqrt{n}}=341+2⋅{24 \over \sqrt{156}}≈345\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval voor het populatiegemiddelde is \([337, 345]\text{.}\)

De steekproefproportie is \(\hat{p}={47 \over 148}=0{,}317...\)

\(\sigma =\sqrt{{\hat{p}(1-\hat{p}) \over n}}=\sqrt{{0{,}317...⋅0{,}682... \over 148}}=0{,}038...\)

\(\hat{p}-2\sigma =0{,}317...-2⋅0{,}038...≈0{,}241\text{.}\)

\(\hat{p}+2\sigma =0{,}317...+2⋅0{,}038...≈0{,}394\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval is \([0{,}241; 0{,}394]\text{.}\)

De steekproefproportie is \(\hat{p}=44\%=0{,}44\text{.}\)

\(\sigma =\sqrt{{\hat{p}(1-\hat{p}) \over n}}=\sqrt{{0{,}44⋅0{,}56 \over 168}}=0{,}0382...\)

\(\hat{p}-2\sigma =0{,}44-2⋅0{,}0382...≈0{,}363\text{.}\)

\(\hat{p}+2\sigma =0{,}44+2⋅0{,}0382...≈0{,}517\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval is \([36{,}3\%; 51{,}7\%]\text{.}\)

\(\hat{p}={0{,}138+0{,}302 \over 2}=0{,}22\) en \(\text{breedte}=0{,}302-0{,}138=0{,}164\text{.}\)

Los op \(4⋅\sqrt{{0{,}22⋅0{,}78 \over n}}=0{,}164\text{.}\)

Voer in
\(y_1=4⋅\sqrt{{0{,}22⋅0{,}78 \over x}}\)
\(y_2=0{,}164\)
Optie 'intersect' geeft \(x=102{,}082...\)

De steekproefomvang is dus \(102\text{.}\)

\(S=66\) en \(\text{breedte}=316-296=20\text{.}\)

Los op \(4⋅{66 \over \sqrt{n}}=20\text{.}\)

Voer in
\(y_1=4⋅{66 \over \sqrt{x}}\)
\(y_2=20\)
Optie 'intersect' geeft \(x=174{,}24\)

De steekproefomvang is dus \(174\text{.}\)