A random variable $X$ is distributed normally with mean $450$ and standard deviation $20$. Fin

Question

A random variable $X$ is distributed normally with mean $450$ and standard deviation $20$. Find $P(X ≤ 475)$.[2] Given that $P(X > a) = 0.27$, find $a$. [4]

Accepted Answer

Since $P(X>a)=0.27$, $P(X\le a)=0.73$ and $z=0.6128$. Thus $a=450+20(0.6128)=462$ approximately.

Calculate a normal probability and an inverse normal quantile.

Calculate a normal probability and an inverse normal quantile.

Solution:

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