Question

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?

Answer 1

Answer: The required lifetime value is 11.27.

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

`x=\mu+z* (\sigma)/(√(n))\\\\x=11+1.645* (1)/(√(36))\\\\x=11+1.645* (1)/(6)\\\\x=11.27`

Hence, the required lifetime value is 11.27.