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:

i’m here for points.

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation: