8.71 Twenty-five lamps are connected so that when one lamp fails, another takes over immediately.

(Only one lamp is on at any one time.) The lamps operate independently, and each has a mean life of 50 hours and a standard deviation of 4 hours. If the system is not checked for 1,300 hours after the first lamp is turned on, what is the probability that a lamp will be burning at the end of the 1,300-hour period?