Question: The Normal approximation (a) A discrete stochastic variable (X) has expected value (mu_{X}=3) and (sigma_{X}=1.2). Use the Normal approximation to find (P(X leq 4)). (b)

The Normal approximation

(a) A discrete stochastic variable $X$ has expected value $\mu_{X}=3$ and $\sigma_{X}=1.2$. Use the Normal approximation to find $P(X \leq 4)$.

(b) A continuous stochastic variable $X$ has expected value $\mu_{X}=3$ and $\sigma_{X}=1.2$. Use the Normal approximation to find $P(X \leq 4)$.

(c) A discrete stochastic variable $X$ has expected value $\mu_{X}=5.1$ and $\sigma_{X}=2.2$. Use the Normal approximation to find $P(X \in\{6,7\})$.

(d) A continuous stochastic variable $X$ has expected value $\mu_{X}=5.1$ and $\sigma_{X}=2.2$. Use the Normal approximation to find $P(X \in(5,7))$.

(e) A discrete stochastic variable $X$ has expected value $\mu_{X}=12.1$ and $\sigma_{X}=4.7$. Use the Normal approximation to find

P = P(X = {12, 13, 14, 15, 16, 17, 18, 19}).

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