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Timer
12-21-2003, 08:12 PM
1. Let's say that I flip a coin 100 times. After 100 flips, should my results lie somewhere between 45 and 55 correct?

2. Now let's say that I have a 57% chance of success on my flips. After 100 flips, will my results now lie somewhere between 52 and 62 correct?

Thanks

Robk
12-22-2003, 12:40 AM
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1. Let's say that I flip a coin 100 times. After 100 flips, should my results lie somewhere between 45 and 55 correct?

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It really depends on what you mean by "should". The standard deviation of a binomial trial is SQRT((np(1-p)) or in your case SQRT (100*1/4) = 5. So the interval from [45, 55] represents one standard deviation from the mean, and the result will be in that range about 68% of the time.

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2. Now let's say that I have a 57% chance of success on my flips. After 100 flips, will my results now lie somewhere between 52 and 62 correct?

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In this example the SD will be = SQRT (100*.57*.43) = 4.95.

If you're interested in similar problems, the sum of n independent identically distributed random variables (coin flips, for example) is approximately normal (as n -&gt; infinity) with mean nu and variance nv where u is the mean of one of the variables and v is the variance of one of the variables (remember they all have the same u and v). If you're curious to know more about how this works post again or search the archives as I'm sure it's come up many times.