Statistics/BINOMDIST/failure rates??

[brokerbrian]

Greetings Power Users!

XP, Excel 2003 with stats ad in

Yes, this is an assignment AND I have the answers BUT I want to know how to get there (not wating your time). Taking online statistics and everyone in class using calculators, I am the only Excel fan.

I approach problem as BINOMDIST and cannot get answers to jive.

80% of new products fail within two years. 66 new products introduced, what is the probability that within 2 years

(a) 47 or more will fail? FALSE = PMF
(b) 58 or fewer will fail? TRUE = CUM
(c) 15 or more will succeed?
(d) fewer than 10 succeed?

Probability = .8, number of trials = 66, 2 years is a distractor, x = period:

(a) does not match key: 1-BINOMDIST(47,66,.8,FALSE)? When equal to or greater than use 1-? Should I use ((47+1),66,etc.?

(b) For fewer, should I use TRUE? Doesn't TRUE indicate value up to x?

(c) duplicate formula and conventions for (a)

(9) should be straight forward but is it TRUE?

As stated, I have the answers from the key, I just want the confirmation of the methodology OR is the answer key wrong (yes, I've seen it before)

Answer Key: (a) .9738 (b) .9599 (c) .3446 (d) .1271

I have been through the fx options for three days and I tried POISSON, and every other tab I could until I just could not syand anymore!

Thanks for your thoughts

 

[xenou]

Hi,
I believe the answer key is wrong.

Taking the last problem as an example, it seems to me that is binomial distribution problem with "success" as .2 (since we are looking at it from the point of few of the product succeeding here). Fewer than 10 succeeding equates to at least 9 succeeding, so we are interested in the cumulative probabilities of 1 succeeding, 2 succeeding, 3 succeeding ... 9 succeeding.

So,
Formula: =Binom.Dist(9,66,.2,True)
Result: 0.124924511

This is not what your answer key gives: 0.1271

I checked it with TI-84 which agrees with Excel:
Formula: =binomcdf(66, .2, 9)
Result: 0.124924511

If that weren't enough, I plugged in the binomial formula "raw" so to speak:
<img alt="binomial function" src="http://mathworld.wolfram.com/images/equations/BinomialDistribution/Inline11.gif" />

This answer agreed closely with Excel:
0.124924109

So much for the answer key.

 

[xenou]

For what it's worth, I often try to rephrase a problem like this:

1) 47 or more will fail --> r <= 19 (p = .2, cumulative, where r is the number of "successes")
Binom.Dist(19, 66, .2, TRUE)

You can also schedule out all 66 trial with the last argument false (not cumulative), and just add up the probabilities with sum formulas - this is a handy way to check the result, and is easy to do with Excel. So, for instance, with the case of 15 or more will succeed, you'd just add up the individual probabilities for 15 through 66, setting p = .2.

I get very confused doing this though - I often do check my results off a schedule of the individual probabilities.
ξ

 

[brokerbrian]

Thank you! I built a P table, just to exercise and got most of the problems to work that way too. I found that if I used for example, the top of the lower P, it matched the bottom of the higher P.

It is challenging trying to build this in Excel, when you're by yourself.