What Your Can Reveal About Your Sampling Distribution From Binomial

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In the following example, we illustrate the sampling distribution for the sample mean for a very small population. People use this type of distribution when they are not well aware of the chosen population or when the sample sizeSample SizeThe sample size formula depicts the relevant population range on which an experiment or survey is conducted.
When estimating p with very rare events and a small n (e. 7% will fall within $[-3,3]$. Here the number of failures is denoted by r. The second video will show the same data but with samples of n = 30.

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6. There are two parameters n and p used here in a binomial distribution.
The rule

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n
p

3
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n
p
(
1

p
)

(
0
,
n
)

{\displaystyle np\pm 3{\sqrt {np(1-p)}}\in (0,n)}

is totally equivalent to request that
Moving terms around yields:
Since

{\displaystyle 0p1}

, we can apply the square power and divide by the respective factors

{\displaystyle np^{2}}

and

n
(
1

)

{\displaystyle n(1-p)^{2}}

, to obtain the desired conditions:
Notice that these conditions automatically imply that

{\displaystyle n9}

. .