the police officer also gathered data on the speedsx, in kilometers per hour (km/h) of some cars as they drove down the hill towards her car. the speed limit is 50 km/h. Analysis of the results showed that the speeds of cars were normally distributed with a mean speed of 56 km/h and a standard deviation of 8 km/h
Cars that exceed the speed limit by 10km/h or more are photographed by a hidden camera. in peak traffic 495 cars pass the camera. how many would be expected to be photographed?
To determine how many cars would be expected to be photographed, we need to calculate the proportion of cars that exceed the speed limit by 10 km/h or more. We can then multiply this proportion by the total number of cars passing the camera.
First, let's calculate the z-score for a speed that exceeds the speed limit by 10 km/h or more. The formula for calculating the z-score is:
z = (x - μ) / σ
where:
- x is the value we want to calculate the z-score for (60 km/h in this case since exceeding the speed limit by 10 km/h results in a speed of 60 km/h for a limit of 50 km/h),
- μ is the mean speed (56 km/h),
- σ is the standard deviation of the speeds (8 km/h).
Using these values, we can calculate the z-score:
z = (60 - 56) / 8
z = 0.5
Next, we need to find the proportion of speeds that exceed the speed limit by 10 km/h or more. We can use a standard normal distribution table or a calculator to find the area under the curve to the right of the z-score. This area gives us the proportion we're looking for.
Using a standard normal distribution table, we can find the area to the right of 0.5, which is approximately 0.30854.
Now, to calculate the number of cars that would be expected to be photographed, we multiply the proportion by the total number of cars passing the camera. In this case, 495 cars pass the camera, so:
Expected number of cars photographed = Proportion * Total number of cars
Expected number of cars photographed = 0.30854 * 495
Expected number of cars photographed ≈ 152.6
Therefore, we would expect approximately 153 cars to be photographed by the hidden camera. Keep in mind that this is an estimate based on the given data.