# Finding Standard Deviation

#### Dason

The 83 might be able to do it directly for you. I don't remember what probability capabilities it had.

#### PhatKroger10

##### New Member
I am kind of confused, is the PHat .05 or .058. I understand the QHat is 1-PHat, but am having difficulties on differentiating which is the PHat.

#### PhatKroger10

##### New Member
http://users.rowan.edu/~schultzl/ti/binomial.pdf

Via the site above my calculator equation shows:
binompdf(500,.05, 29)=.0552
n=500, p=.05, x=29, p=.0552

I entered this online in my homework and it said that it was incorrect. Is there something I am doing wrong here?

#### BGM

##### TS Contributor
Ok I double check your work in R once more:

> dbinom(29,500,0.05)
[1] 0.05520704

Maybe that online question really want you to use the normal approximation. The approximation is not very good as the binomial distribution is (highly) skewed and it is near the tail area.

Caution: Here is the computation in R with continuity correction. Only check it when you have try the hints given by Dason - computing the mean and variance, and understanding the usage of Central Limit Theorem.

> pnorm((29.5-25)/sqrt(23.75))-pnorm((28.5-25)/sqrt(23.75))
[1] 0.05841719

#### Strong Fort

##### New Member
It's definitely a binomial probability problem. Using a simple online calculator you can find "the probability that exactly 29 of the 500 calculators will be returned for refund or replacement within a 2-year period" - P = 5.52%. Standard deviation of binomial distribution is equal to s=sqrt[ n * p * ( 1 - p ) ]. In our case n=500, p=0.05 so we have s=4.87.