a. Parameterize by
with .
b/c. The line integral of over
is
d. Notice that we can write the line integral as
By Green's theorem, the line integral is equivalent to
where is the triangle bounded by
, and this integral is simply twice the area of
.
is a right triangle with legs 2 and 5, so its area is 5 and the integral's value is 10.
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.