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A Car Dealership Has Found That the Length of Time

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A car dealership has found that the length of time before a major repair is required on the new cars it sells is normally distributed, with a mean equal of 36 months and a standard deviation of 9 months. If the dealer wants only 5% of the cars to fail before the end of the guarantee period, for how many months should the cars be guaranteed?
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Definitions:

Mammogram

A breast X-ray used as a diagnostic and screening tool to detect breast cancer and other abnormalities in breast tissue.

Transfer Order

An instruction to move something or someone from one place to another, often used in the context of hospital patients or goods in logistics.

Discharge Instructions

Written or verbal instructions given to a patient upon discharge from a healthcare facility, outlining care procedures, medications, follow-up appointments, and activity restrictions.

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A broad category of brain diseases that cause long-term and often gradual decrease in the ability to think and remember, significantly affecting a person's daily functioning.

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