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The lifetime of a machine follows a normal distribution with the average life of 12.01 years and the standard deviation of 3.23 years. The manufacturer

The lifetime of a machine follows a normal distribution with the average life of 12.01 years and the standard deviation of 3.23 years. The manufacturer replaces free all machines that fail while under guarantee. If she is willing to replace only 1.5% of the machines that fail, how long a guarantee should be offered?

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