Question

LED light bulbs are manufactured with an average life span of 16 years and the bulb lifespans are known to follow an exponential distribution.
a. What is the probability that a bulb will last longer than 14 years?
b. What is the 50th percentile (or median) of bulb lifespans?

Answer 1

P (x>14)=e^(-14/16)= 0.4169=41.6%

P(X>/=k)
Solve for K as K will be the median value.

e^(-k/16)=1/2
Shorthand to find the median of an exponential distr. is:
Meanxln(2)=k

meaning 16xln2=11.09
This is the value of a median, not a percentage.