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The weights of a group of children are approximately normally distributed with mean 15kg and standard deviation=1.75 kg What proportion of the children will weigh 13 of or more?

Can someone help me solve it?

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1 Answer 1

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Let $Y \sim \mathcal{N}(15,1.75^{2})$ be a normal distributed random variable with mean $15$ and variance $1.75^{2}$. Then you have to compute

\begin{align} \mathbb{P}(Y \geq 13) &= \mathbb{P}(\frac{Y - 15}{1.75} \geq -\frac{8}{7})\\ &= 1 - \Phi(-\frac{8}{7})\\ &= 1 - (1 - \Phi(\frac{8}{7}))\\ &= \Phi(\frac{8}{7})\\ &\approx 0.87345 \end{align} where $\Phi$ is the Cumulative distribution function of the Standard normal random variable with mean $0$ and variance $1$.

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