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Consider the following measures of the filling level in mm during a bottling process:
230.7, 229.4, 230.6, 231.0, 229.8, 229.7, 230.5, 229.9, 230.1, 229.9, 230.1, 229.6.
(a) Transfer the data into a software tool (R or MATLAB) and find an appropriate
graphical representation.
(b) Investigate whether a normal distribution fits to the data.
(c) Estimate the mean, the variance and the standard deviation of the distribution.
(d) Assume a normal distribution for the filling level and estimate the range which
covers 95% of the filling levels.
Tip: The R function pnorm(x, mu, sigma) provides the distribution function F(x) =
P(X ≤ x) for a normally distributed random variable with mean mu and standard deviation sigma. The corresponding MATLAB command is normcdf with the same arguments.
The normal- and t-quantile functions are qnorm and qt in R respectively norminv and
tinv in MATLAB.