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Q42Section C (Section C)42 of 60

Probability from a base ten lognormal variable

If Y=log⁡10XY=\log_{10}X has N(μ,σ2)N(\mu,\sigma^2) distribution with moment generating function MY(t)=e5t+2t2M_Y(t)=e^{5t+2t^2}, t∈(−∞,∞)t\in(-\infty,\infty), then P(X<1000)P(X<1000) equals __________________

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