Answer:
Step-by-step explanation:
y′′ + 4y′ − 21y = 0
The auxiliary equation is given by
m² + 4m - 21 = 0
We solve this using the quadratic formula. So
So, the solution of the equation is
where m₁ = 3 and m₂ = -7.
So,
Also,
Since y(1) = 1 and y'(1) = 0, we substitute them into the equations above. So,
Substituting A into (1) above, we have
Substituting B into A, we have
Substituting A and B into y, we have
So the solution to the differential equation is
Answer:
Approximately normal
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation
In this question:
As the sample size is above 30, even though the underlying distribution is right-skewed, the shape of the sampling distribution of the sample means will be approximately normal.