normal approximation to the binomial

I know this should be easy but I'm not seeing it.

Question: On average, 3% of the watches manufactured by a particular company will be returned for warranty repair. Use the normal approximation to the binomial to find the probability that among 1000 watches sold, 40 or fewer will be returned.

I have that 3% of 1000 is 30 which is my mean.

So, (40-30)/$\displaystyle \sigma$=probability

And I'm stuck here, because I can't see the standard deviation. Once I have that I can get a value that I can look up in the tables, correct?

Any help would be appreciated.

Re: normal approximation to the binomial

Quote:

I can't see the standard deviation

use the standard deviation of the binomial distribution you are trying to approximate, which is $\displaystyle \sqrt{np(1-p)}$

I think you mean (40-30)/http://www.mathhelpforum.com/math-he...293c147d21.png = Z

and you intend to look up the probability associated with the Z value in your tables.

**PS **Do you need a continuity correction?

Re: normal approximation to the binomial

Thank you.

(40-30)/15.8=.6329 I looked up .6329 and came up with a probability of .7357.

Re: normal approximation to the binomial

IIRC, you need a continuity correction.

Re: normal approximation to the binomial

(40.5-30)/15.8=.6646 with Probability = .7454

Thank you.