Suppose that the longevity of a light bulb is exponential with a mean lifetime of eight years. Seventy percent of all light bulbs last at least how long?

Using the exponential distribution, it is found that 70% of all light bulbs last at least 2.85 years.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:  

In which is the decay parameter.

The probability that x is lower or equal to a is given by:

Which has the following solution:

The probability of finding a value higher than x is:

In this problem, the mean lifetime is of 8 years, hence .

Seventy percent of all light bulbs last at least x, considering that .

Hence:

70% of all light bulbs last at least 2.85 years.

To learn more about the exponential distribution, you can take a look at link