One company produces movie trailers with mean 150 seconds and standard deviation 40 seconds, while a second company produces movie trailers with mean 120 seconds and standard deviation 30 seconds. What is the probability that two randomly selected trailers, one produced by each company, will combine to less than three minutes? Assume each distribution is normal.

3 minutes = 180 seconds

Assuming that each company will contribute equally, you want to find the probability of < 90 seconds for each company. (However, you realize it might be a 80/100, 85/95, et cetera splits.)

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability for each Z score.

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

To find the probability that two randomly selected trailers, one produced by each company, will combine to less than three minutes, we need to find the combined distribution of the two trailer lengths.

First, let's convert three minutes to seconds: 3 minutes * 60 seconds/minute = 180 seconds.

Now, let's calculate the mean and standard deviation of the combined distribution:

Mean of the combined distribution = Mean of company A + Mean of company B = 150 seconds + 120 seconds = 270 seconds.

Standard deviation of the combined distribution = Square root of (Standard deviation of company A squared + Standard deviation of company B squared) = Square root of (40^2 + 30^2) = Square root of (1600 + 900) = Square root of 2500 = 50 seconds.

Now, we have the mean and standard deviation of the combined distribution, and we can use the z-score formula to find the probability.

Z-score = (x - mean) / standard deviation.

In this case, we want to find the probability of the combined length being less than 180 seconds.

Z-score = (180 - 270) / 50 = -90 / 50 = -1.8.

Using a standard normal distribution table or a calculator, we can find the probability associated with the z-score of -1.8.

The probability associated with a z-score of -1.8 is approximately 0.0359.

Therefore, the probability that two randomly selected trailers, one produced by each company, will combine to less than three minutes is approximately 0.0359, or 3.59%.