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Tutorial 6 An automatic machine in a manufacturing process is

Tutorial 6

An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed, with mean ? = 117 cm and standard deviation ? = 2.1 cm.

If the machine is operating correctly:

(i) Find the probability that one randomly selected unit has a length greater than 120 cm;

(ii) Find the probability that if three units are randomly selected, their mean length exceeds 120 cm;

(iii) Explain the differences between parts (i) and (ii).

(iv)Referring to your answers above, draw the probability density function of the length of a subcomponent in (i) and that of the mean of three subcomponents in (ii) on a single axis.

(v) Is the distribution of the sample mean less or more variable than the distribution of the parent population? Explain your answer.


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