Review this and improve it in any way if there are any errors: Using the GRASS Format solve this:A police speed camera is set up to monitor vehicles on a stretch of road with aspeed limit of 40 km/h. Long-term records for this location show that speedsfollow a normal distribution with a mean of 48 km/h, and a standard deviation of 6km/h. The speed camera will automatically ticket all drivers who exceed the limitby more than 10%. What percent of drivers will receive a ticket? (9 marks)

ChatGPT said: ChatGPT To solve this using the GRASS format, we'll go through each step as follows:

G – Given: Mean speed (μ): 48 km/h Standard deviation (σ): 6 km/h Speed limit: 40 km/h Drivers are ticketed if they exceed the speed limit by more than 10%. R – Required: We need to find the percentage of drivers who will receive a ticket. In other words, we need to calculate the probability of a driver exceeding 10% above the speed limit.

A – Approach: First, calculate the speed threshold for ticketing:

The speed limit is 40 km/h. 10% over the speed limit is: 40 × 1.1

44 40×1.1=44 km/h. Therefore, drivers will be ticketed if they exceed 44 km/h. Find the z-score for this speed using the normal distribution formula:

𝑧

𝑥 − 𝜇 𝜎 z= σ x−μ ​

Where:

𝑥 x is the speed threshold (44 km/h). 𝜇 μ is the mean (48 km/h). 𝜎 σ is the standard deviation (6 km/h). Use the z-score to find the corresponding percentile using standard normal distribution tables or a calculator.

S – Solution: Calculate the z-score:

𝑧

44 − 48 6

− 4 6

− 0.67 z= 6 44−48 ​

6 −4 ​ =−0.67 Use a standard normal distribution table (or calculator) to find the probability corresponding to a z-score of -0.67.

A z-score of -0.67 corresponds to a cumulative probability of approximately 0.2514. This means that about 25.14% of drivers are driving at or below 44 km/h. To find the percentage of drivers exceeding 44 km/h, subtract this probability from 1:

𝑃 ( drivers exceeding 44 km/h )

1 − 0.2514

0.7486 P(drivers exceeding 44 km/h)=1−0.2514=0.7486 So, approximately 74.86% of drivers will receive a ticket.

S – Statement: Approximately 74.86% of drivers will receive a ticket based on the speed camera's threshold.