Question 1136800
mean = n * p = 200 * .2 = 20


standard deviation = sqrt( n * p * q ) = sqrt( 200 * .2 * .8 ) = 5.656854249.


i believe that's the answer you're looking for.


here's a reference.


<a href = "https://stattrek.com/probability-distributions/binomial.aspx" target = "_blank">https://stattrek.com/probability-distributions/binomial.aspx</a>


in your binomial distribution:


n = 200
p = .1
q =.9
mean = 200 * .10 = 20
standard deviation is sqrt (200 * .2 * .8) = 5.656854 rounded to 3 decimal places.


the variance is equal to n * p * q.
the standard deviation is the square root of the variance which makes it equal to sqrt (n * p * q).


this forms a normal distribution where the mean is 20 and the standard deviation is 5.656854.


about 68.3% of the defects will be centered within 1 standard deviation from the mean.


<img src = "http://theo.x10hosting.com/2019/031701.jpg" alt="$$$" >


about 95.4% of the defects will be centered within 2 standard deviations from the mean.


<img src = "http://theo.x10hosting.com/2019/031702.jpg" alt="$$$" >


about 99.7% of the defects will be centered within 3 standard deviations from the mean.


<img src = "http://theo.x10hosting.com/2019/031703.jpg" alt="$$$" >


the normal distribution calculator i used can be found at <a href = "http://davidmlane.com/hyperstat/z_table.html" target = "_blank">http://davidmlane.com/hyperstat/z_table.html</a>