# normal approximation to the binomial

• Jul 25th 2011, 08:37 AM
CountingPenguins
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)/ $\sigma$=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.
• Jul 25th 2011, 08:48 AM
SpringFan25
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 $\sqrt{np(1-p)}$

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?
• Jul 25th 2011, 09:12 AM
CountingPenguins
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.
• Jul 25th 2011, 11:35 AM
SpringFan25
Re: normal approximation to the binomial
IIRC, you need a continuity correction.
• Jul 25th 2011, 12:02 PM
CountingPenguins
Re: normal approximation to the binomial
(40.5-30)/15.8=.6646 with Probability = .7454

Thank you.