A lighting vendor has described its incandescent bulbs as having normally distributed lifetimes with a mean of 2000 hours and a standard deviation of 100 hours. The vendor is faced with an especially demanding industrial customer who insists on conducting a longevity test before committing to a very large order. The customer's purchasing department plans to test a simple random sample of 16 bulbs and to place the large order only if the sample mean is at least 2050 hours.
Given the longevity of the vendor's bulbs and the test the potential customer will be carrying out, what is the probability that the vendor will get the contract?