The Lifespans of a Particular Brand of Graphing Calculator Are

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.