Question

If the lifetime X of a certain kind of automobile battery is normally distributed with a mean of 5 years and a standard deviation of 1 year, and the manufacturer wishes to guarantee the battery for 4 years, what percentage of the batteries will he have to replace under the guarantee?

          If the lifetime X of a certain kind of automobile battery is normally distributed with a mean of 5
years and a standard deviation of 1 year, and the manufacturer wishes to guarantee the battery for 4
years, what percentage of the batteries will he have to replace under the guarantee?

If the lifetime X of a certain kind of automobile battery is normally distributed with a mean of 5
years and a standard deviation of 1 year, and the manufacturer wishes to guarantee the battery for 4
years, what percentage of the batteries will he have to replace under the guarantee?

Added by Misty R.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Michael Anderson

04/04/2022

Step 1

Step 1: Calculate the z-score for the value 4 years using the formula: \( z = \frac{x - \mu}{\sigma} \), where \( x = 4 \), \( \mu = 5 \), and \( \sigma = 1 \). Show more…

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If the lifetime X of a certain kind of automobile battery is normally distributed with a mean of 5 years and a standard deviation of 1 year, and the manufacturer wishes to guarantee the battery for 4 years, what percentage of the batteries will he have to replace under the guarantee?