Briefing:

A laboratory testing process for an intensive care unit is normally distributed with an average turnaround time of 10 minutes and a standard deviation of 5 minutes. The upper acceptable limit requested by the intensive care unit for the laboratory testing process is 12 minutes.

Question: The Management decided that reducing standard deviation this much is nearly impossible. To reduce the probability of not meeting the upper acceptable limit, intensive care unit decided to build another lab that will work in parallel to the first lab. This means that both labs will start testing at the same time and they stop when either one of them is done. The second lab also has a mean process time of 10 minutes with a standard deviation of 5 minutes. What is the probability that the turnaround time of the laboratory testing process exceeds upper acceptable limit?