Copy Machines a Manufacturer Claims That Lifespans for Their Copy

question 54

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 a several large office buildings buys 200 of these copiers. The salesman tells the boss "190 (95%) of your new copiers will last between _____ and _____ 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.

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Definitions:

Arnold Gesell

An American psychologist and pediatrician known for his pioneering work in child development and promoting the concept that child growth unfolds predictably and sequentially in several domains.

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The evaluation of actions and reactions in specific scenarios to assess various psychological conditions or developmental stages.

Infant Testing

Methods designed to evaluate developmental stages, cognitive abilities, and physical growth in babies and very young children.

Divergent Thinking

Thinking that produces many answers to the same question; characteristic of creativity.