The beverage manufacturer acquires another machine. It is assumed that the filling quantities of all bottles are independent of each other. The continuous random variable $Y$: ``Filling quantity of a randomly selected bottle filled by this machine'' is assumed to be normally distributed with expected value $\mu = 331$ [ml] and standard deviation $\sigma = 1.34 [ \mathrm { ml } ]$. A filling with at most 327 ml is referred to in the following as a severe underfilling.
(1) Determine the probability that a randomly selected bottle is a severe underfilling.
Give your result rounded to five decimal places.
[Check solution with four decimal places: 0.0014.]
(2) Determine the expected number of severe underfilled bottles in a sample of 1500 bottles.
(3) Determine the probability that a sample of 750 bottles contains more than two severe underfilled bottles.
(4) The beverage manufacturer changes the machine parameters to $\mu _ { \text {new } } = 330 [ \mathrm { ml } ]$ and $\sigma _ { \text {new } } = 1.00 [ \mathrm { ml } ]$.
Interpret the changed parameters in the given context.
Assess how the probability that a randomly selected bottle is a severe underfilling changes due to the change in parameters.