The manager of a supermarket tracked the amount of time needed for customers to be served by the cashier. After checking with his statistics professor, he concluded that the checkout times are exponentially distributed with a mean of 6.5 minutes. What propotion of customers require more than 11 minutes to check out

For this case we want to find this probability:

And we can use the cumulative distribution given by:

The mean is given by:

And then

And replacing we got:

Step-by-step explanation:

Previous concepts

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

Solution to the problem

For this case we can define the random variable X= "checkout times"

And the distribution for X is given by:

For this case we want to find this probability:

And we can use the cumulative distribution given by:

The mean is given by:

And then

And replacing we got: