Let x follow a Normal distribution with mean 2 and variance 4. This question is not a duplicate. One question is stating between two variables
Basic stats question having trouble figuring this out.
2026-03-28 22:26:53.1774736813
What is the probability that x is less than 5.92?
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Hint:
$$Pr(X < 5.92) = Pr\left(\frac{X-2}{2} < \frac{5.92-2}{2}\right)$$
and
$$\frac{X-2}{2} \sim N(0,1)$$
Edit:
Such values are usually found by using statistical tables (e.g. http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf [Credit:JMoravitz] )
$$\frac{5.92-2}{2}=1.96$$
Reading from the table, $F_Z(1.96) = 0.975 $ which is the value that you want to find.
Remark: $1.96$ is a "special" value as it is commonly used in constructing $95\%$ confidence interval.