Let the random variable $X$ be normally distributed with mean $25$, as shown in the following di

Question

Let the random variable $X$ be normally distributed with mean $25$, as shown in the following diagram. The shaded region between $25$ and $27$ represents $30 \%$ of the distribution. Find $P(X > 27)$.[2] Find the standard deviation of $X$. [5]

Accepted Answer

Since $P(X<27)=0.8$, $\frac{27-25}{\sigma}=z_{0.8}=0.8416$. Thus $\sigma=2.38$.

Use normal symmetry and an inverse probability to determine a standard deviation.

Use normal symmetry and an inverse probability to determine a standard deviation.

Solution:

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