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.

Question

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.

PsyDAG · Answer

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.