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.

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.