A Cutting Tool Has a Lifetime That Is Normally Distributed

question 2

Essay

A cutting tool has a lifetime that is normally distributed with an average life of 400 hours and a standard deviation of 50 hours.Present policy is preventive maintenance which requires changing all cutting tools at the end of each month.Current operations are two shifts per day and 7 working hours per shift.At 20 days per month,each cutting tool is in use 280 hours per month.(All cutting tools that fail are simply shut down until the end of the month sweep).The variable costs of replacement under the current policy are $8 per tool plus installation labor of $6 per tool.There are 40 tools in use.
-What is the likelihood that a cutting tool will fail during the month?

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Definitions:

Functional Autonomy

A principle in psychology where behaviors continue to serve a purpose independent of their original motivator.

Healthy Adults

Individuals who have reached maturity not only in biological terms but also exhibit psychological well-being and appropriate coping mechanisms.

Psychological Forces

Internal or external factors that influence an individual's mental states and behaviors.

Proprium

Refers to the aspects of a person's self or personality that contribute to their sense of identity and continuity over time.