The set of life spans of an appliance is normally distributed with a mean mu is equal to 48 months and a standard deviation sigma is equal to 8 months. What is the life span of an appliance that has a z -score of negative 3 ?

Use the z-score relationship x = μ + zσ. With a mean of 48 months, a standard deviation of 8 months, and z = −3, the life span is 48 + (−3)(8) = 24 months. So the appliance’s life span is 24 months.

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