Copy Machines a Manufacturer Claims That Lifespans for Their Copy $\underline{\quad\quad}$

question 38

Essay

Copy machines A manufacturer claims that lifespans for their copy machines (in months)can be described by a Normal model N(42, 7). Show your work.
a. Draw and clearly label the model.
b. A company with several large office buildings buys 200 of these copiers. The salesman tells the boss "190 (95%) of your new copiers will last between $\underline{\quad\quad}$ and $\underline{\quad\quad}$ months." Comment on this claim.
c. What is the 3rd quartile of copier lifespans?
d. What percent of the copiers are expected to fail before 36 months?
e. The manufacturer wants to reduce the 36-month failure rate to only 10%. Assuming the mean lifespan will stay the same, what standard deviation must they achieve?
f. Briefly explain what that change in standard deviation means in this context.
g. A competing manufacturer says that not only will 90% of their copiers last at least 36 months, 65% will last at least 42 months. What Normal model parameters is that manufacturer claiming? Show your work. N( $\underline{\quad\quad}$ , $\underline{\quad\quad}$ )

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Definitions:

Horney's Theory

A psychoanalytic theory by Karen Horney focusing on social and cultural factors affecting personality, introducing the concepts of basic anxiety and neurotic needs.

Locus of Control

The extent to which individuals believe that they can control events that affect them, with variations ranging from internal (personal control) to external (control by external forces).

Behavioral Evidence

Observational data pertaining to actions and reactions that provide insight into underlying psychological processes or conditions.

Social Cognitive Theory

A theory that emphasizes the importance of observational learning, imitation, and modeling in understanding behavior.