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%Solution to Quiz #1
%We have the weights (using cut and paste!)
weights=[159 
   110 
   171 
   199 
   129 
   176 
   188 
   102 
   107 
   167 
   138 
   171 
   174 
   171 
   189 
   170 
   186 
   114 
   149 
   145 ];

%Now for question 1:
ave=mean(weights)
stdev=std(weights)

%you could also do this directly via:
n=length(weights)
ave=sum(weights)/n
stdev=((norm(weights)^2-ave^2*n)/(n-1))^.5
%Which yields the same result...

%note that matlab uses the correct n-1 normalization for the standard deviation.
%Type in "help std" and "help mean" for more information...

%Now for question 2:

%We will exceed 900 lb if the average weight of the five (m) exceeds 180 lb.  The 
%standard deviation of the -average- of five students (assuming independence) is
%reduced from the population standard deviation by (m)^.5.  Thus, we can use the
%error function to get the answer:
m=5;
probover=1-0.5*(1+erf((180-ave)*m^.5/stdev/2^.5))

%Note that the probability we are -over- this amount is 1-prob of being under...

%And finally for question 3: 
%The three assumptions are: independence, normal distribution, and accuracy of
%population mean and standard deviation estimates.

%a). Independence.  Student weights (among the five) can be either positively or 
%negatively covariant.  If positive (birds of a feather flock to an elevator together)
%then we underestimate the standard deviation and probability.  If negative (a large
%student is unlikely to squeeze into a packed elevator) we overestimate the standard
%deviation and probability.  This is the sort of biased sampling issue you run into in
%many types of experiments.

%b). Normal distribution.  Our overall probability is fairly low, thus we are on
%the tail of the gaussian normal distribution.  In general, this means that the
%gaussian probability is likely to underestimate the true probability.

%c). Assumption of accuracy of population estimates.  The values calculated for (1)
%have error in them as well - thus error in these estimates means that the
%probability estimate is itself a random variable.  We will look at calculating
%the confidence interval of the probability estimate in a later quiz.

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