The cycle time required to manufacture a complex engine part

The cycle time required to manufacture a complex engine part can vary depending on many factors, including tool wear, part temperature, ambient temperature, humidity, etc.
a)Describe the sample space for this variable.

b)Three events are defined:
L: less than 8 hours
S: More than 7 hours but less than or equal to 7.5 hours
E: More than 7.5 hours

Are any pair of intervals mutually exclusive? If so, which ones?

c)Three additional events are of interest.
0: engine part has no defects
1: engine part needs to be reworked
2: engine part must be scrapped.

List the sample space (all possible outcomes) for a part.

Solution

a)Here the cycle time is the variable therefore the sample space is the value of time required to manufacture a complex engine

b)In logic and probability theory, two propositions (or events) are mutually exclusive or disjoint if they cannot both be true (occur).Here the time interval for the 7-7.5 hour and more than 7.5 hour are mutually exclusive as both cannot occur at the same time

c)The sample space for the part is as noted---no defects, one or more defects requiring rework and sufficient defects to be rendered scrap.