The assembly of a machine requires two stages, that proceed consecutively and independently of one another. The first stage takes a mean time of 20 minutes with a standard deviation of 8 minutes. The second stage takes a mean of 30 minutes with a standard deviation of 12 minutes. The next 100 machines assembled will be sent in a shipment to Portland.
And the question:
What is the probability that the total time spent assembling 100 machines is less than 80 hours?
I am not 100% sure on how to go about solving this problem as an example does not exist within my professors notes, however my intuition is telling me to create a normal variable with the mean being the sum of both stages means, and the variance being the sum of squared SDs and then using a normal cumulative distribution function to solve for the probability p(X<80)… Am I on the right track or am I completely off?
Thank you in advance for any help provided!