# Moivre-Laplace theorem (homework)

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1. Apr 24, 2015

### Poetria

< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >

I have no idea what I am doing wrong. Here is my problem:

S(n) - the number of successes in 10 Bernoulli trials, each with probability 0.7

I am supposed to use normal approximation to compute :

P{|S(n)/10-0.7|>0.2}

We are allowed to use a calculator.

I got:
|S(n)-7|>2|
5<S(n)>9

I have computed S*:

S(n)-7/1.44914
7=mean
1.44914- standard deviation

5*1.44914-7<Z<9*1.44914-7

Area (probability): 0.2451

But there is no such answer in the options.

Last edited by a moderator: Apr 24, 2015
2. Apr 24, 2015

### SammyS

Staff Emeritus
What do you mean by 5<S(n)>9 ?

That's an invalid compound inequality.

3. Apr 24, 2015

### Poetria

I see. :( My line of thought was as follows:

S(n)-7>2 or S(n)-7<-2 (this is an absolute value equation: |S(n)/10-0.7|>0.2)

How to correct it?

4. Apr 24, 2015

### SammyS

Staff Emeritus
What you have here is correct.

S(n)-7>2 or S(n)-7<-2

That says S(n) > 9 or S(n) < 5 . (You had S(n) > 5 )

You can't make these into a compound inequality.

5. Apr 24, 2015

### Ray Vickson

Last edited: Apr 24, 2015
6. Apr 25, 2015

### Poetria

Thank you so much. I have tried to work it out. I think I got it. My problem is that I still can't get an exact answer. The closest (with the correction you have suggested):
if x = 5.5 I get 0.15031188 (I can choose 0.1675)
http://www.danielsoper.com/statcalc3/calc.aspx?id=53

The result: 0.08377348 is very imprecise.
Actually some calculators demand x, some Z. It is a mess.

7. Apr 25, 2015

### Poetria

Sorry, I get 0.71860226. Even worse.

8. Apr 25, 2015

### Poetria

I got it at last. :) Many thanks. :) You have helped me a lot. :) :) :)