<p>The random variable $X$ is normally distributed with mean $135$ and variance $\sigma^{2}$.</p>
<ol class="i-list"><li><div class="list-item-paragraph">Given that $\mathrm{P}\left( 127 a \right)=0.3865$, show that $\sigma =10.68$, correct to the $2$ decimal places, and find the value of the constant $a$.</div></li></ol>
<p>$X$ is related to a normal random variable $Y$ by the formula $X=Y_{1}+Y_{2}-4$, where $Y_{1}$ and $Y_{2}$ are two independent observations of $Y$.</p>
<ol class="i-list" start="2"><li><div class="list-item-paragraph">Find $\mathrm{E}(Y)$ and $\mathrm{Var}(Y)$.</div></li></ol>

The random variable $X$ is normally distributed with mean $135$ and variance $\sigma^{2}$.

Given that $\mathrm{P}\left( 127 a \right)=0.3865$, show that $\sigma =10.68$, correct to the $2$ decimal places, and find the value of the constant $a$.

$X$ is related to a normal random variable $Y$ by the formula $X=Y_{1}+Y_{2}-4$, where $Y_{1}$ and $Y_{2}$ are two independent observations of $Y$.

Find $\mathrm{E}(Y)$ and $\mathrm{Var}(Y)$.

Continuous Random Variables

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Operations, Applications, and Parameter Inference

Operations, Applications, and Parameter Inference

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