1. A random sample of 25 lightbulbs was taken from a normal population and it was found that the mean lifetime of a certain bulb for a movie projector is 520 hours with a standard deviation of 50 hours. The manufacturing company claims that the lifetime of this type of bulb is more than 500 hours. Does the data support the company's claim at a level of significance of = .10? Provide a supporting explanation and show your work.