Answer :
Question: The probability that cars passing a speed camera are speeding is 0.25. If 752 cars pass the camera, how many of the cars would you expect to be speeding and what would be the variance?
To find the number of cars you would expect to be speeding, we can use the formula for expected value (E(X)). The expected value represents the average value we would expect to see if the experiment is repeated many times.
The formula for expected value is: E(X) = n * p, where n is the number of trials and p is the probability of success.
In this case, the number of cars passing the camera is 752 and the probability of a car speeding is 0.25. Therefore, we can calculate the expected value as follows:
E(X) = 752 * 0.25 = 188
So, you would expect 188 cars to be speeding.
Next, let's calculate the variance (V(X)). The variance measures how spread out the values are around the expected value.
The formula for variance is: V(X) = n * p * (1 - p).
Using the same values as before, we can calculate the variance as follows:
V(X) = 752 * 0.25 * (1 - 0.25) = 141
So, the variance would be 141.
Therefore, the correct answer is:
E(X) = 188 and V(X) = 141.
Learn more about probability : https://brainly.com/question/13604758
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