06

TD 6

Exo 34

\(X \sim \mathcal{N}(\mu,\frac{\sigma^{2}}{50})\)

1

\(\hat{\mu} = x\)

2

\(\frac{D - \mu}{\frac{\sigma}{\sqrt{n}}} \sim \mathcal{N}(0,1)\)
\({\mathbb{P}}( - t_{0.95} \leq \frac{D - \mu}{\frac{\sigma}{\sqrt{50}}} \leq t_{0.95}) = 0.95\)
\({\mathbb{P}}( - 1.96 \leq \frac{D - \mu}{\frac{\sigma}{\sqrt{50}}} \leq 1.96) = 0.95\) (D’après le cours)
Après calculs:
\({\mathbb{P}}(9.94 \leq \mu \leq 10.04)\)

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