Question

recall from earlier quizzes that you have a safe filled with an enormous amount of money in bills of different denominations. Suppose one day you count all the bills, keeping track of denominations. You learn that the mean value of a bill in your safe is $34.80, and the standard deviation is $38.15. You program the distribution into Stata and tell it to run a Monte Carlo simulation on the sample mean of a sample of size 144, with a billion simulation draws( you do not actually have to do anything in Stata to answer this question). In other words, the computer will take 1 billion random sample of size 144 from your distribution, compute the sample mean for each, then give you information on the resulting distribution. What will be the 90th percentile in the Stata summary of the simulation results for X-bar? Round to TWO decimal places.

Answer 1

Sampling Distribution

Sample Mean = 34.8

Standard deviation = 38.15 / sqrt(144)

=38.15 / 12

=3.1792

µ=   34.8                  
σ =    3.1792   
proportion=   0.9                  
                      
Z value at    0.9   =   1.28   (excel formula =NORMSINV(   0.9   ) )
z=(x-µ)/σ                      
so, X=zσ+µ=   1.28   *   3.179166667   +   34.8  
X   =   38.87   (answer)          

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