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We're currently handling normal distribution in class but I'm missing the clue I guess.

We get an assignment like: Calculate the follwing chances: P(X > 85)

This was my solution: Solution

It's given that µ = 70, and G = 10 (standard deviation). We also know that Z must be 1.5 than, because 85 is 1.5 times the standard deviation away from µ.

Than I use the formula: z = (x - µ) / G; do some algebra on it until I get the result x = 85.

However, now I just calculated X, that was not the assignment... What step am I missing to calculate the probability that X > 85?

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  • $\begingroup$ Use the statistical tables to find $P(Z>1.5)$. $\endgroup$
    – user371838
    Dec 6, 2017 at 11:35

1 Answer 1

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If $X\sim N(70,100)=N(\mu,G^2)$, then $Z= \frac{X-70}{10}\sim N(0,1)$ and thus \begin{align} P(X>85)=P\Big(\frac{X-70}{10}>\frac{85-70}{10}\Big)=P(Z>1.5) \end{align} The complementary event of $\lbrace Z>1.5\rbrace$ is $\lbrace Z\leq 1.5\rbrace$ and thus \begin{align} P(Z>1.5)=1-P(Z\leq 1.5) \end{align} Now look into a statistical table! The Keyword is $N(0,1)$-distribution.

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