표본평균 확률로 표본 크기

$\displaystyle \mathrm{E} ( \overline{X} ^{)} = m$, $\displaystyle \sigma ( \overline{X} ^{)} = \frac{3}{\sqrt{n}}$이므로 확률변수 $\displaystyle \overline{X}$는 정규분포 $\displaystyle \mathrm{N} \left( m , \left( \frac{3}{\sqrt{n}} \right) ^{2} \right)$을 따른다. $\displaystyle \mathrm{P} ( m - 0.5 \leq \overline{X} ^{\leq} m + 0.5 )$ $\displaystyle = \mathrm{P} ( | \overline{X} ^{-m} | \leq 0.5 )$ $\displaystyle = \mathrm{P} \left( | Z | \leq \frac{\sqrt{n}}{6} \right)$ $\displaystyle \left( \because \frac{| \overline{X} ^{-m} |}{\frac{3}{\sqrt{n}}} \leq \frac{0.5}{\frac{3}{\sqrt{n}}} \right)$ $\displaystyle \mathrm{P} \left( | Z | \leq \frac{\sqrt{n}}{6} \right) = 0.8664$ $\displaystyle \mathrm{P} \left( 0 \leq Z \leq \frac{\sqrt{n}}{6} \right) = 0.4332$ $\displaystyle \frac{\sqrt{n}}{6} = 1.5$, $\displaystyle \sqrt{n} = 9$ $\therefore n = 81$