The speeds of cars at a certain point on a straight road are normally distributed with mean $\mu$

Question

The speeds of cars at a certain point on a straight road are normally distributed with mean $\mu$ and standard deviation $\sigma$. Fifteen percent of the cars travel faster than $90\text{ km h}^{-1}$, and 12% travel slower than $40\text{ km h}^{-1}$. Find $\mu$ and $\sigma$.

Accepted Answer

Using $z_{0.85}=1.0364$ and $z_{0.12}=-1.1750$ gives $\sigma=22.6\text{ km h}^{-1}$ and $\mu=66.6\text{ km h}^{-1}$.

Determine a normal mean and standard deviation from two tail percentages.

Determine a normal mean and standard deviation from two tail percentages.

Solution:

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