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

Transcribed Image Text:

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