In tests on a new type of light bulb it was found that the time they lasted followed a normal distribution with standard deviation 40.6 hours. 10% lasted longer than 5130 hours.

1. Find the mean lifetime, giving your answer to the nearest hour.
2. Find the probability that a light bulb fails to last for 5000 hours.
3. A hospital buys 600 of these light bulbs. Using a suitable approximation, find the probability that fewer than 65 light bulbs will last longer than 5130 hours.