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.

Question

25-10-2022
Mathematics

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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.

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MounaH555861 MounaH555861 · Answer 1 · 2022-10-25T12:31:38+02:00

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

[tex]P\left(x>z\right)=0.05[/tex]

Therefore; using a z score calculator, this gives;

[tex]z=1.645[/tex]

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

[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \end{gathered}[/tex]

Since

[tex]\begin{gathered} \mu=$ 300,000. $ \\ \sigma=58,000 \end{gathered}[/tex]

Therefore, we will have

[tex]\begin{gathered} 1.645=\frac{x-300000}{58000} \\ \mathrm{Switch\:sides} \\ \frac{x-300000}{58000}=1.645 \\ crossmutiply \\ x-300000=58000\times1.645 \\ x=300000+95410 \\ x=395410 \end{gathered}[/tex]

Answer: 395410