A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a standard deviation of 55 minutes with a mean life of 1141 minutes. If the claim is true, in a sample of 55 batteries, what is the probability that the mean battery life would be greater than 1132.1 minutes? Round your answer to four decimal places.

And using the complement rule and a calculator, excel or the normal standard table we have that:

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

Where and

For this case the distribution for the sample mean is given by:

We can find the individual probabilities like this:

And using the complement rule and a calculator, excel or the normal standard table we have that:

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step-by-step explanation: