Answer:

And using the cdf 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:

And 0 for other case. Let X the random variable that represent the random variable of interest and we know that the distribution is given by:

We know the variance on this case given by :

So then the deviation is given by:

And if we solve for
we got:

The cumulative distribution function for the exponential distribution is given by:

Solution to the problem
And for this case we want to find this probability:

And using the cdf we got:

4/15 because it can't be reduced any more. I hope this helps you out! :D
Answer:
6.07/212
Step-by-step explanation:
P(x)=R(x)-C(x)
=(-0.5x²+800x-100)-(300x+250)
=-0.5x²+800x-100-300x-250
=-0.5x²+800x-300x-100-250
=-0.5x²+500x-350 (2)