Hello i am doing assignment in my math 20-2 class. The question is: data collected of cars passing on the road revealed that the average speed was 90 km/h with a standard deviation of 5 km/h and the data which is normally distributed a policeman is assigned to set photo radar on the road in which the posted speed limit is 80 km/h it's 600 cars pass the photo radar in the police man sets the camera so that only those exceeding the speed limit by 10% are photographed, then how many drivers can the police expect to ticket? Can someone please tell me how to solve this?

Question

Hello i am doing assignment in my math 20-2 class. The question is: data collected of cars passing on the road revealed that the average speed was 90 km/h with a standard deviation of 5 km/h and the data which is normally distributed a policeman is assigned to set photo radar on the road in which the posted speed limit is 80 km/h it's 600 cars pass the photo radar in the police man sets the camera so that only those exceeding the speed limit by 10% are photographed, then how many drivers can the police expect to ticket? Can someone please tell me how to solve this?

Answer 1

Z = (score-mean)/SD

If the camera is set at 10% above speed limit = 88 km/h.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability in the larger portion related to the Z score. Multiply by 600.

Answer 2

Ok but before we start we usually write downwhat the mean equals, standard deviation and X. Im still confused on which one would be the mean.

Answer 3

I found that the inversenorm is 83.5922, what do i do after this?

Answer 4

To solve this problem, we can start by finding the average speed and standard deviation of the cars exceeding the speed limit by 10%.

1. First, calculate the speed limit plus 10%: 80 km/h + (10% of 80 km/h) = 88 km/h.
2. To find the average speed of cars exceeding the speed limit by 10%, subtract the speed limit from the average speed: 90 km/h - 88 km/h = 2 km/h.
3. Next, to find the standard deviation of cars exceeding the speed limit by 10%, we subtract the speed limit from the average speed and the standard deviation: 5 km/h - 2 km/h = 3 km/h.

Now, we need to convert the problem into a standard normal distribution and then use the Z-table to find the probability. Since the problem states that only those exceeding the speed limit by 10% are photographed, we want to find the probability of cars exceeding 88 km/h (converted from 80 km/h) in the normal distribution.

4. Calculate the Z-score using the formula: Z = (X - μ) / σ, where X is the value (88 km/h), μ is the mean (average speed of cars exceeding the speed limit by 10% = 2 km/h), and σ is the standard deviation (3 km/h).

Z = (88 km/h - 2 km/h) / 3 km/h

Now you can divide 88-2 by 3.
5. Use the Z-table or a calculator to find the probability associated with the Z-score you calculated. In this case, it represents the probability of a car exceeding the speed limit by 10%.

For example, if the Z-score calculates to be 2, the Z-table can give you the probability value associated with that Z-score.

6. Once you have the probability, multiply it by the total number of cars passing the photo radar (600) to find the expected number of drivers to be ticketed.

For instance, if the probability is 0.05 (5%), you can calculate as follows: 0.05 * 600 = 30.

Therefore, the police can expect to ticket approximately 30 drivers.

Remember, the Z-table provides the probability for a standard normal distribution. However, since we convert our problem into a standard normal distribution, we can use the Z-table to find the probability associated with the Z-score.