the lifetime of a certain battery has an unknown distribution with mean value 8 hours and...

the lifetime of a certain battery has an unknown distribution with mean value 8 hours and a standard deviation of 2 hours. what is the probability that the average battery lifetime of a sample of 36 batteries will be greater than 8.1 hours?

I know by the CLT that at 36 trials the sample mean will follow a normal distribution but i cant remember how to calculate the variance of this distribution nor do i know where to go from there. Thanks.

Expert Solution

Solution :

= / n = 2 / 36 = 0.3333

P( 8.1) = 1 - P( 8.1)

= 1 - P[( - ) / (8.1 - 8) / 0.3333]

= 1 - P(z 0.30)

= 0.3821

Probability = 0.3821

orchestra answered 2 years ago

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