Apologies for the bad handwriting.
Answer:
The standard error of the mean is 0.0783.
Step-by-step explanation:
The Central Limit Theorem helps us find the standard error of the mean:
The Central Limit Theorem estabilishes that, for a random variable X, with mean
and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
.
The standard deviation of the sample is the same as the standard error of the mean. So

In this problem, we have that:

So



The standard error of the mean is 0.0783.
Answer:
Both
and
are solutions to the system.
Step-by-step explanation:
In order to determine whether the two given points represent solutions to our system of equations, we must "plug" thos points into both equations and check that the equality remains valid.
Step 1: Plug
into 

The solution verifies the equation.
Step 2: Plug
into 

The solution verifies both equations. Therefore,
is a solution to this system.
Now we must check if the second point is also valid.
Step 3: Plug
into 

Step 4: Plug
into 

The solution verifies both equations. Therefore,
is another solution to this system.