Finding Standard Deviation

Dason

Ambassador to the humans
#21
The 83 might be able to do it directly for you. I don't remember what probability capabilities it had.
 

BGM

TS Contributor
#24
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
 
#25
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.