Forty-nine heat lamps are connected in a greenhouse so that when one lamp fails, another takes over immediately and only one lamp is on at any given time. The lamps operate independently, and each has a mean life of 80 hours and a standard deviation of 4 hours.

If the greenhouse is not checked for 4000 hours after the lamp system is turned on, what is the probability that a lamp will be burning at the end of the 4000 hour period?