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The lifetime of a certain type of battery is normally distributed with mean value 11 hours and standard deviation 1 hour. There are nine batteries in a package. What lifetime value is such that the total lifetime of all batteries in a package exceeds that value for only 5% of all packages?

Respuesta :

Answer: The required lifetime value is 11.27.

Step-by-step explanation:

Since we have given that

Mean value = 11 hours

Standard deviation = 1 hour

The total lifetime of all batteries in a package exceeds that value for only 5% of all packages.

So, α = 0.95, z= 1.645

n = 9

So, the lifetime value would be

[tex]x=\mu+z\times \dfrac{\sigma}{\sqrt{n}}\\\\x=11+1.645\times \dfrac{1}{\sqrt{36}}\\\\x=11+1.645\times \dfrac{1}{6}\\\\x=11.27[/tex]

Hence, the required lifetime value is 11.27.

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