5.8. A machine fills packages of flour. The exact quantity that is filled into the packages follows a normal distribution with mean 1003 g and standard deviation 5g. a) Calculate the probability that the filled quantity is less than 995g. b) Calculate the approximate probability that the filled quantity is between 1001.35 and 1001.45g without using R. c) Find the filling quantity that is exceeded by 99% of all packages.

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Chapter1: Combinatorial Analysis
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5.8. A machine fills packages of flour. The exact quantity that is filled into the packages
follows a normal distribution with mean 1003 g and standard deviation 5g.
a) Calculate the probability that the filled quantity is less than 995g.
b) Calculate the approximate probability that the filled quantity is between
1001.35 and 1001.45g without using R.
c) Find the filling quantity that is exceeded by 99% of all packages.
d) If a package is filled with less than 990g a fine of 10$ has to be paid. Find the
expectation and the variance of the fine for 500 filled packages.
Transcribed Image Text:5.8. A machine fills packages of flour. The exact quantity that is filled into the packages follows a normal distribution with mean 1003 g and standard deviation 5g. a) Calculate the probability that the filled quantity is less than 995g. b) Calculate the approximate probability that the filled quantity is between 1001.35 and 1001.45g without using R. c) Find the filling quantity that is exceeded by 99% of all packages. d) If a package is filled with less than 990g a fine of 10$ has to be paid. Find the expectation and the variance of the fine for 500 filled packages.
Start the solution of such problems always by defining
the random variate X, that can be used to solve the problem
and finding the distribution and the parameters of that RV!
Transcribed Image Text:Start the solution of such problems always by defining the random variate X, that can be used to solve the problem and finding the distribution and the parameters of that RV!
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