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Find expectation, variance and probability sample mean in range for normal distribution, ,
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Normal distribution $X \sim N(\mu,\sigma^2)$ given. Find $P(a \lt X \lt b)$. Find expectation, variance, $P(c \lt \overline{X} \lt d)$ for sample mean $\overline{X}$.

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