Let $X$ be normally distributed with a mean of $105$ and standard deviation of $10$.
- What is the probability that $X > 112$?
- What value of $X$ does only the top $5\%$ exceed ?
2026-04-02 11:10:22.1775128222
Distribution and Standard deviation
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ok.
Using standardization that is
$$Z=\frac{X-\mu}{\sigma}$$
you can use Z-score to calculate probablities...
thus
$$P(X<112)=P\left(Z<\frac{112-105}{10}\right)$$
and obviously
$$P(X>112)=1-P(X<112)$$
The second question is an inverse Z-score problem...they give you the probability and you have to calculate the quantile