The length of time spent waiting in line at a certain bank is modeled by an exponential density function with a mean of 5 minutes. Find the probability that you would wait in line for at least 8 minutes in this bank.

And for this case we can use the complement rule and we got:

And we can use also the cumulative distribution function given by:

And replacing we got:

Step-by-step explanation:

For this case we can define the random variable of interest X as "The length of time spent waiting in line at a certain bank" and for this case we know that the distribution for X is given by:

And for this case we want to find the following probability:

And for this case we can use the complement rule and we got:

And we can use also the cumulative distribution function given by:

And replacing we got: