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Answer:
(1) A Normal approximation to binomial can be applied for population 1, if <em>n</em> = 100.
(2) A Normal approximation to binomial can be applied for population 2, if <em>n</em> = 100, 50 and 40.
(3) A Normal approximation to binomial can be applied for population 2, if <em>n</em> = 100, 50, 40 and 20.
Step-by-step explanation:
Consider a random variable <em>X</em> following a Binomial distribution with parameters <em>n </em>and <em>p</em>.
If the sample selected is too large and the probability of success is close to 0.50 a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:
- np ≥ 10
- n(1 - p) ≥ 10
The three populations has the following proportions:
p₁ = 0.10
p₂ = 0.30
p₃ = 0.50
(1)
Check the Normal approximation conditions for population 1, for all the provided <em>n</em> as follows:
Thus, a Normal approximation to binomial can be applied for population 1, if <em>n</em> = 100.
(2)
Check the Normal approximation conditions for population 2, for all the provided <em>n</em> as follows:
Thus, a Normal approximation to binomial can be applied for population 2, if <em>n</em> = 100, 50 and 40.
(3)
Check the Normal approximation conditions for population 3, for all the provided <em>n</em> as follows:
Thus, a Normal approximation to binomial can be applied for population 2, if <em>n</em> = 100, 50, 40 and 20.
Answer:
603.71
Step-by-step explanation:
Use a function to solve this.
F(x)
Now lets put in the data for the function.
We have 910, which is the orginal number. This should be the first number, and will have to be multiplyied by the other numbers in the function to find the answer. I think of all these numbers like the things in a penut butter and jelly sandwhich, is sounds very nice since I am hungry.
F(x) = 910 *
Next, we have 5%, which is what we are taking from 910. So, we can think of this as 910 being multiplyied by 0.95. Lets add this to our growing penut butter and jelly sandwhich. The reason I put this into a parenthese is so that the 910
F(x) = 910 * (0.95)
Now for the last step, we must add in the years. So, eahc year we reduce the 910 by 5%, and we need to do this 8 years This means that the 910 times 0.95 must repeat 8 times. To do this, we need ot use exponent. This exponent is 8. So, here is our completed function:
F(x) = 910 * (0.95^8)
Lets plug this into a calculator, since doing this out on paper would be a real pain and will take far to long. I would probably die of hunger and never get a penut butter and jelly sandwhich if I did this out on paper.
In the end, you should get 603.7125 blah blah blah it goes on for a long time. I attached a file of what it looks like in the calculator if you want some evidence.
Oh, you said you want it rounded to the nearest whole number. Well, lets remember our rounding here. Anything below 5 goes down, anything 5 and higher goes up. Since we have 603.7125, we can round that too 603.71
Answer:
<u>603.71</u>
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Im gonna go grab my PBJ now.
