Many electronic devices use disposable batteries, whicheventually have to be replaced. Assume that for oneparticular brand and type of battery, the distribution ofthe hours of useful power can be approximated well by aNormal model. The mean is 140 hours, and the standarddeviation is 4 hours.a) Using the 68-95-99.7 Rule, sketch the appropriatemodel.b) The marketing department wants to write a guaranteefor battery life. What lifespan should they quote sothat they can expect 98% of the batteries to meet theguarantee?c) The company’s research department has been giventhe task of improving the batteries, with a goal thatat least 90% of the new batteries should last longerthan the average of the current type. Initial researchsuggests that a mean of 143 hours is attainable. Whatother improvement must they make to achieve theirgoal?d) Explain what the improvement you suggest in part cwould mean about the new batteries.

Many electronic devices use disposable batteries, which
eventually have to be replaced. Assume that for one
particular brand and type of battery, the distribution of
the hours of useful power can be approximated well by a
Normal model. The mean is 140 hours, and the standard
deviation is 4 hours.
a) Using the 68-95-99.7 Rule, sketch the appropriate
model.
b) The marketing department wants to write a guarantee
for battery life. What lifespan should they quote so
that they can expect 98% of the batteries to meet the
guarantee?
c) The company’s research department has been given
the task of improving the batteries, with a goal that
at least 90% of the new batteries should last longer
than the average of the current type. Initial research
suggests that a mean of 143 hours is attainable. What
other improvement must they make to achieve their
goal?
d) Explain what the improvement you suggest in part c
would mean about the new batteries.

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