A random variable $X$ is distributed normally with a mean of $20$ and variance $9$. Find \(P(X

Question

A random variable $X$ is distributed normally with a mean of $20$ and variance $9$. Find $P(X ≤ 24.5)$.[3] Let $P(X ≤ k) = 0.85$. [5] Represent this information on the following diagram. Find the value of $k$.

Accepted Answer

For $P(X\le k)=0.85$, $z_{0.85}=1.0364$, so $k=20+3(1.0364)=23.1$.

Calculate a normal probability and determine an unknown quantile from a shaded curve.

Calculate a normal probability and determine an unknown quantile from a shaded curve.

Solution:

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