Newsgroup sci.stat.math 11648

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> Can you help me solve this question?
> 
> In the Persian Gulf War, the United States used Patriot missiles as a way to defent the 
> Iraqi SCUD missile. The manufacturer claims a Patriot missile fired has a 60% chance of 
> destroying its target. Now suppose a sculd missile has been detedted and four Patriot 
> missiles are fired at the SCUD. Find the probability that the SCUD is destroyed. Please 
> show you work. The choices are:
> A) .9744
> B) .9375
> C) .1296
> D) .8704
> 
> How many Patriot missiles would need to be fired to increase the chance of the SCUD 
> being destroyed to at least .99? Please show you work. The choices are:
> 
> A) 9
> B) 8
> C) 7
> D) 6
> E) 5
I haven't found a simple equation to determine the number of missiles
needed for a given degree of assurance.  However, it can be done easily
enough by iterating the equation n=a+b+ab, and finding it through trial
and error.
For two missiles, a and b each equal .6, yielding .84.
For four missiles, a and b each equal .84, yielding .9744.
For five missiles, a equals .6, and b equals .9744, yielding .98976.
For six missiles, a equals .84, and b equals .9744 yielding .995904.
Therefore, the answer is D-6.
Allen D. Montgomery

jjboeldt@in.net wrote:
> 
> > Can you help me solve this question?
> >
> > In the Persian Gulf War, the United States used Patriot missiles as a way to defent the
> > Iraqi SCUD missile. The manufacturer claims a Patriot missile fired has a 60% chance of
> > destroying its target. Now suppose a sculd missile has been detedted and four Patriot
> > missiles are fired at the SCUD. Find the probability that the SCUD is destroyed. Please
> > show you work. The choices are:
> > A) .9744
> > B) .9375
> > C) .1296
> > D) .8704
> >
> > How many Patriot missiles would need to be fired to increase the chance of the SCUD
> > being destroyed to at least .99? Please show you work. The choices are:
> >
> > A) 9
> > B) 8
> > C) 7
> > D) 6
> > E) 5
A simple way of looking at it is that n Patriot missiles
acting independently have a probability of .4^n of not
destroying the SCUD which means 1-.4^n of destroying it.
 1-.4^4 = .9744.
The second part calls for the smallest n such that
 .4^n <=.01 which is 6.

I’m trying to complete an Elementary Statistics course by correspondence
and I'm really having a tough time of it. I have 24 more questions to
complete and I am really having a tough time. I'f I share the questions
can anyone walk me through the steps to answering them?

Have you tried a non-parametric test such as the Wilcoxon rank-sum? Just
looking at your values, I can see that you reach the maximum possible
statistic for that method since there is no overlap in the data for the
two groups.
Regards, David.
In article <01bbcdcc$54d6b400$4a276682@s317109.slip.cc.uq.edu.au>, "Andrew
"  wrote:
> Here is Some More info on the Analysis:
> 
> Five transgenic seedlings were grown on medium containing no inducer. These
> seelings were removed individually and assayed for presence of the enzyme
> after 48 hours (a process which kills the seedlings).  This gave five
> results (one for each seedling).
> 
> Another Five transgenic seedlings (from the same seedstock) were germinated
> on medium with a suspected inducer. These seedlings were removed
> individually and assayed after 48 hours.  This gave another five results
> (one for each transgenic seedling)
> 
> The enzyme measurement was quantitative, measuring the specific amount of
> enzyme produced
> 
> Here is a sample of the data (each seedling gave one value):
> 
> Treated enzyme activity: 107.0, 83.9, 106.9, 680.7 & 38.25
> 
> Untreated enzyme activity: 26.9, 3.8, 20.8, 37.5 & 15.1 
> 
> The values would appear to show an induction of the gene. but the
> heteroscedastic t-test (i assume this test is valid) shows that the
> difference is not significant.  The treated data have a lot of variation
> because the plants are at an early growth stage and the number of gene
> inserts within the plants vary.
> 
> I hope this is enough info.
> 
> Andrew Morgan
> University of Queensland
> 
> PS.  If your interested the transgene is a reporter gene -defence promoter
> construct.  We've joined the promoter sequence of a defence gene to the
> sequence of  an enzyme (beta-glucuronidase) which we can assay for
> expression levels, and put it back into the plants.
-- 
David Winsemius, MD, MPH
dwinsemius@imagine.com
"...the greatest invention in human history was compound interest."
                  -- Albert Einstein --

>jjboeldt@in.net wrote:
> Can you help me solve this question?
>
> In the Persian Gulf War, the United States used Patriot missiles as a way 
> to defent the Iraqi SCUD missile. The manufacturer claims a Patriot missile 
> fired has a 60% chance of destroying its target. Now suppose a sculd missile
> has been detedted and four Patriot missiles are fired at the SCUD. Find the 
> probability that the SCUD is destroyed. Please show you work. The choices 
> are:
>
> A) .9744
> B) .9375
> C) .1296
> D) .8704
In article <32853A0A.618E@access.digex.net>,
Ellen Hertz   wrote:
>
>A simple way of looking at it is that n Patriot missiles
>acting independently have a probability of .4^n of not
>destroying the SCUD which means 1-.4^n of destroying it.
This is almost certainly wrong, however, since there is every reason
to think that the failure of one Patriot to destry the missile is not
independent of the failure of another.  For example, the Patriot might
have a 100% success rate in good weather, and a 0% success rate in
bad weather.  If good weather occurs 60% of the time and bad weather
40% of the time, the chance of a single Patriot destroying the missile
will be the advertised 60%.  Firing more than one will not improve the
chances at all.
The correct answer is:
  E) Cannot be determined from the available information
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Radford M. Neal                                       radford@cs.utoronto.ca
Dept. of Statistics and Dept. of Computer Science radford@utstat.utoronto.ca
University of Toronto                     http://www.cs.utoronto.ca/~radford
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