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

Question

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

Accepted Answer

Using $90=\mu+z_{0.85}\sigma$ and $40=\mu+z_{0.12}\sigma$ 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:

Solution locked