The natural logarithm of the lifetime (i.e., take the natural log of the lifetime, in hours) of a certain type of bulb is found to be normally distributed with a mean of 13 hours and a standard deviation of 1.5 hours. What is the probability that: (a) One randomly selected bulb of this type survives 2.5 years of use. (b) At least one in two of this type of bulb will survive 2.5 years of use. (c) How many bulbs of this type shall be installed in a room to guarantee 99.99% reliability that at least one can light the room after 3 years?

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