De steekproefproportie is \(\hat{p}={46 \over 144}=0{,}319...\)

\(\sigma =\sqrt{{\hat{p}(1-\hat{p}) \over n}}=\sqrt{{0{,}319...⋅0{,}680... \over 144}}=0{,}038...\)

\(\hat{p}-2\sigma =0{,}319...-2⋅0{,}038...≈0{,}242\text{.}\)

\(\hat{p}+2\sigma =0{,}319...+2⋅0{,}038...≈0{,}397\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval is \([0{,}242; 0{,}397]\text{.}\)

De steekproefproportie is \(\hat{p}=39\%=0{,}39\text{.}\)

\(\sigma =\sqrt{{\hat{p}(1-\hat{p}) \over n}}=\sqrt{{0{,}39⋅0{,}61 \over 248}}=0{,}0309...\)

\(\hat{p}-2\sigma =0{,}39-2⋅0{,}0309...≈0{,}328\text{.}\)

\(\hat{p}+2\sigma =0{,}39+2⋅0{,}0309...≈0{,}452\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval is \([32{,}8\%; 45{,}2\%]\text{.}\)

\(\bar{X}-2⋅{S \over \sqrt{n}}=2{,}85-2⋅{0{,}59 \over \sqrt{163}}≈2{,}76\text{.}\)

\(\bar{X}+2⋅{S \over \sqrt{n}}=2{,}85+2⋅{0{,}59 \over \sqrt{163}}≈2{,}94\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval voor het populatiegemiddelde is \([2{,}76; 2{,}94]\text{.}\)

\(\hat{p}={0{,}354+0{,}486 \over 2}=0{,}42\) en \(\text{breedte}=0{,}486-0{,}354=0{,}132\text{.}\)

Los op \(4⋅\sqrt{{0{,}42⋅0{,}58 \over n}}=0{,}132\text{.}\)

Voer in
\(y_1=4⋅\sqrt{{0{,}42⋅0{,}58 \over x}}\)
\(y_2=0{,}132\)
Optie 'intersect' geeft \(x=223{,}691...\)

De steekproefomvang is dus \(224\text{.}\)

\(S=8{,}4\) en \(\text{breedte}=51{,}5-48{,}3=3{,}2\text{.}\)

Los op \(4⋅{8{,}4 \over \sqrt{n}}=3{,}2\text{.}\)

Voer in
\(y_1=4⋅{8{,}4 \over \sqrt{x}}\)
\(y_2=3{,}2\)
Optie 'intersect' geeft \(x=110{,}25\)

De steekproefomvang is dus \(110\text{.}\)