2. f(x) = 3(x - 2)2 + 6a. Standard Form:
1 answer:
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Answer:
a)
b)
c)
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".
Part a
Let X the random variable that represent the number of people of a population, and for this case we know that:
Where and
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
From the central limit theorem we know that the distribution for the sample mean is given by:
And we want to find this probability:
And using a calculator, excel or the normal standard table we have that:
Part b
And using a calculator, excel or the normal standard table we have that:
Part c
For this case we want this probability:
And using a calculator, excel or the normal standard table we have that:
Answer:
All solutions
Step-by-step explanation:
When solving by substitution, we will first set one equation equal to a variable, and then plug that value into the second equation as the variable. Here is what I mean;
x - 2y = 1
3x - 6y = 3
-
x = 1 + 2y
3x - 6y = 3
-
3(1 + 2y) - 6y = 3
3 + 6y - 6y = 3
3 = 3
[] Oh no! This doesn't work well. Let's graph it and see what is happening;
-> See attached
-> I have made the lines very thick so you can see the overlap, they are the same size in reality
The answer is all solutions because the graphs are exactly the same.
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.
- Heather
