Answer:
Where 
and 
Since the distribution for X is normal then the distribution for the sample mean is also normal and given by:
So then is appropiate use the normal distribution to find the probabilities for 
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean". The letter 
is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: 
Solution to the problem
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
Where and
Since the distribution for X is normal then the distribution for the sample mean is also normal and given by:
So then is appropiate use the normal distribution to find the probabilities for
ANSWER
x coordinates of the intersection points
EXPLANATION
The given system of equations is:
We want to use the graph of these functions to solve
The point of the intersection of the graph gives the solution to the simultaneous equation above.
Hence the x-coordinates of the intersection points gives the solution set of
The last choice is correct.
So first off the equation we are solving is f(x) + g(x). So i want to plug in those equations first off. The new equation I get should be 3x-2 + 6 -4x. I then simplify this to -x+4 or 4-x.
Answer:
And we can find this probability with this difference:
And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the costs of services of a population, and for this case we know the distribution for X is given by:
Where 
and 
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability with this difference:
And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.
