A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a standard deviation of 6262 minutes with a mean life of 606606 minutes. If the claim is true, in a sample of 9999 batteries, what is the probability that the mean battery life would be greater than 619619 minutes

And we want to find the following probability:

And we can use the z score formula given by:

And replacing we got:

And we can use the normal standard distirbution and the complement rule to find the probability:

Step-by-step explanation:

For this problem we have the following parameters given:

represent the mean

represent the true deviation

represent the sample size

For this case since the sample size is >30 we can use the central limit theorem and we can u se the following distribution for the sample mean

And we want to find the following probability:

And we can use the z score formula given by:

And replacing we got:

And we can use the normal standard distirbution and the complement rule to find the probability:

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step-by-step explanation: