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?
To solve this problem, you need to follow these steps:
Step 1: Find the mean speed of the cars passing.
The average speed is given as 90 km/h.
Step 2: Determine the standard deviation.
The standard deviation is given as 5 km/h.
Step 3: Calculate the speed limit after applying the 10% excess.
The speed limit is 80 km/h. To find the speed limit with a 10% excess, multiply it by 1.1.
Speed limit with 10% excess = 80 km/h * 1.1 = 88 km/h.
Step 4: Calculate the z-score.
The z-score measures how many standard deviations a value is from the mean. It is calculated using the formula:
z = (x - μ) / σ,
where x represents the value, μ represents the mean, and σ represents the standard deviation.
In this case, using the speed limit with 10% excess (88 km/h):
z = (88 - 90) / 5 = -2 / 5 = -0.4.
Step 5: Determine the proportion of cars exceeding the speed limit.
To find this, you need to use a standard normal distribution table or a calculator. The table or calculator will give you the proportion of the area under the curve to the left of the z-score.
Consulting the table or calculator, you will find that the proportion of cars exceeding the speed limit (z = -0.4) is approximately 0.3446.
Step 6: Calculate the number of drivers expected to be ticketed.
Multiply the proportion from the previous step by the number of cars passing the photo radar (600):
Expected number of drivers to be ticketed = 0.3446 * 600 = 206.76.
Since you cannot have a fraction of a driver, round to the nearest whole number.
So, the police can expect to ticket approximately 207 drivers.
In conclusion, the police can expect to ticket approximately 207 drivers exceeding the speed limit by 10%.