\(\bar{X}-2⋅{S \over \sqrt{n}}=751-2⋅{134 \over \sqrt{104}}≈725\text{.}\)

\(\bar{X}+2⋅{S \over \sqrt{n}}=751+2⋅{134 \over \sqrt{104}}≈777\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval voor het populatiegemiddelde is \([725, 777]\text{.}\)

De steekproefproportie is \(\hat{p}={24 \over 224}=0{,}107...\)

\(\sigma =\sqrt{{\hat{p}(1-\hat{p}) \over n}}=\sqrt{{0{,}107...⋅0{,}892... \over 224}}=0{,}020...\)

\(\hat{p}-2\sigma =0{,}107...-2⋅0{,}020...≈0{,}066\text{.}\)

\(\hat{p}+2\sigma =0{,}107...+2⋅0{,}020...≈0{,}148\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval is \([0{,}066; 0{,}148]\text{.}\)

De steekproefproportie is \(\hat{p}=31\%=0{,}31\text{.}\)

\(\sigma =\sqrt{{\hat{p}(1-\hat{p}) \over n}}=\sqrt{{0{,}31⋅0{,}69 \over 161}}=0{,}0364...\)

\(\hat{p}-2\sigma =0{,}31-2⋅0{,}0364...≈0{,}237\text{.}\)

\(\hat{p}+2\sigma =0{,}31+2⋅0{,}0364...≈0{,}383\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval is \([23{,}7\%; 38{,}3\%]\text{.}\)

\(\hat{p}={0{,}070+0{,}170 \over 2}=0{,}12\) en \(\text{breedte}=0{,}170-0{,}070=0{,}1\text{.}\)

Los op \(4⋅\sqrt{{0{,}12⋅0{,}88 \over n}}=0{,}1\text{.}\)

Voer in
\(y_1=4⋅\sqrt{{0{,}12⋅0{,}88 \over x}}\)
\(y_2=0{,}1\)
Optie 'intersect' geeft \(x=168{,}96\)

De steekproefomvang is dus \(169\text{.}\)

\(S=123\) en \(\text{breedte}=802-758=44\text{.}\)

Los op \(4⋅{123 \over \sqrt{n}}=44\text{.}\)

Voer in
\(y_1=4⋅{123 \over \sqrt{x}}\)
\(y_2=44\)
Optie 'intersect' geeft \(x=125{,}033...\)

De steekproefomvang is dus \(125\text{.}\)