Question

Speeding tickets provide a significant source of revenue for many American cities. For one city in South Florida, the average annual speeding ticket revenue per police officer is $300,000. The standard deviation for these annual speeding ticket revenues is $58,000. If these amounts have a normal distribution, find the cutoff amount of annual speeding ticket revenue that separates the highest five percent of revenue generating officers from the other ninety-five percent.

Answer 1

Step-by-step explanation

To find the cutoff amount of annual speeding ticket revenue that separates the highest five percent of revenue-generating officers from the other ninety-five percent.

We will need to find

`P\left(x>z\right)=0.05`

Therefore; using a z score calculator, this gives;

`z=1.645`

We can then find the cutoff amount z using the formula below;

`\begin{gathered} z=(x-\mu)/(\sigma) \\ \end{gathered}`

Since

`\begin{gathered} \mu=$ 300,000. $ \\ \sigma=58,000 \end{gathered}`

Therefore, we will have

`\begin{gathered} 1.645=(x-300000)/(58000) \\ \mathrm{Switch\:sides} \\ (x-300000)/(58000)=1.645 \\ crossmutiply \\ x-300000=58000*1.645 \\ x=300000+95410 \\ x=395410 \end{gathered}`

Answer: 395410