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The standartization of $X$ is given by $$Z=\frac{X-\mu}{\sigma},$$ where $\mu=\operatorname EX$ and $\sigma^2=\operatorname{Var}X$. We have that $$P(Z\le z)=P\biggl(\frac{X-\mu}{\sigma}\le z\biggr)=P(X\le \sigma z+\mu)$$ and we know that $X\sim\mathcal N(\mu,\sigma^2)$. Hence, $$P(X\le \sigma z+\mu)=\frac1{\sigma\sqrt{2\pi}}\int_{-\infty}^{\sigma ... 1 Suppose there are n flowers. The number of flowers still blossoming at time t is a random variable X(t), equal to$$X(t)=\sum_{f=1}^n I(\text{flower $f$ is alive at time $t$})\tag1$$where the indicator function I(A) equals one if event A is true, zero otherwise. The expectation of X(t) is then$$E(X(t))=n P(\text{flower $1$ is alive at time ...

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Hint:$$\Phi^{-1}(U)\leq x\iff U\leq \Phi(x)$$ Here $\Phi$ denotes the CDF corresponding with standard normal distribution.

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It is a one-dimensional normal distribution. https://en.wikipedia.org/wiki/Cram%C3%A9r%E2%80%93Wold_theorem This follows from an alternative definition of multi-dimensional Gaussian distribution. EDIT: see the Wikipedia article (for future reference/anyone new to the question) https://en.wikipedia.org/wiki/Multivariate_normal_distribution#Definition

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