## A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a standard deviation of 6

Question

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? Round your answer to four decimal places.

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1 month 2021-10-22T00:38:22+00:00 1 Answer 0 views 0

0.0183 = 1.83% probability that the mean battery life would be greater than 619 minutes

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by: The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that: What is the probability that the mean battery life would be greater than 619 minutes?

This is 1 subtracted by the pvalue of Z when X = 619. So By the Central Limit Theorem    has a pvalue of 0.9817

1 – 0.9817 = 0.0183

0.0183 = 1.83% probability that the mean battery life would be greater than 619 minutes