The Lifespans of a Particular Brand of Graphing Calculator Are

question 106

Essay

The lifespans of a particular brand of graphing calculator are approximately normally distributed with a mean of 620 days from the purchase date and a standard deviation of 82 days. They will provide a warranty that guarantees a replacement if the calculator stops working within the specified time frame, and are trying to decide what time frame to use. a. If the company sets the warranty at a year and a half (say 540 days), what proportion of calculators will they have to replace?
b. The company does not want to have to replace more than 1% of the calculators they sell. What length of time should they set for the warranty?
c. The company would like to set the warranty for 540 days, and still replace no more than
1% of the calculators sold. Increasing the average life of the calculators is too expensive, but
they think they reduce the standard deviation of the lifespans. What standard deviation of lifespans would be needed to make this happen?
d. Explain what achieving a smaller standard deviation means in this context.

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Definitions:

Start-Up Process

The series of steps undertaken by entrepreneurs to establish a business, which includes ideation, market research, planning, funding, and launching operations.

Maturity

The stage in life or condition when development is complete and stable, often associated with full growth or an ability to reproduce.

Relative Certainty

The degree of confidence or assurance one has regarding the occurrence of an event or the truth of a statement, often compared to other scenarios or information.

Licensing Agreement

An agreement in which the owner of intellectual property grants another person (or another company) permission to produce that product.