We are given that the average life of a one-dollar Federal Reserve note is 22 months. We need to show that at most 37% of one-dollar bills last for at least five years.
Let X be the lifetime (in months) of randomly selected dollar bill. Then, we need to show that.
To show the given inequality, we need to use Markov’s Inequality as for nonnegative random variable X and.
For, we have
Since we have, we get
On simplifying, we get
Thus, at most 37% of one-dollar bills last for at least five years.