Can someone show me how to do this problem?

A manufacturer claims that it's light bulbs have a mean lifetime of 1550 hours with a standard deviation of 75 ours. A random sample of 50 bulbs is selected for testing. If the sample produces a mean of 1435.8 hours, is there sufficient evidence to reject the manufacturer's claim? Use alpha = .01.

Find the 97% confidence interval of the population, "u"

Please and thank you!