Question

Twenty-five heat lamps are connected in a greenhouse so that when one lamp fails, another takes over immediately. (Only one lamp is turned on at any time.) The lamps operate independently, and each has a mean life of 90 hours and standard deviation of 5 hours. If the greenhouse is not checked for 2,325 hours after the lamp system is turned on, what is the probability that a lamp will be burning at the end of the 2325-hour period? (Round your answer to four decimal places.)

Answer 1

Solution :

Given that ,

= 90

= / n = 5 / 25 = 1

= 2325 / 25 = 93

P( > 93) = 1 - P( < 93)

= 1 - P[( - ) / < (93 - 90) / 1 ]

= 1 - P(z < 3.0)   

= 1 - 0.9987

= 0.0013