# The mean lifetime of a tire is 39 months with a variance of 81. If 127 tires are sampled, what...

## Question:

The mean lifetime of a tire is 39 months with a variance of 81.

If 127 tires are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 0.4 months? Round your answer to four decimal places.

## Sampling distributions and the central limit theorem:

When a sample of size {eq}n \geq 30 {/eq} is drawn from any population which has a specified population mean and a specified population variance, then the sampling distribution of the sample means is an approximately normal distribution. As the sample size increases, the approximation gets better and closer to a normal distribution. If the population itself follows a normal distribution, then the sampling distribution of the sample means is also normal. In both cases, the sampling distribution of the sample means has a mean that is always equal to the population mean and a variance equal to {eq}1/n {/eq} times the population variance. This is the central limit theorem (CLT).

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The probability that the mean lifetime of the sample would differ from the population mean by less than 0.4 months is 0.6915.

Step 1:

We are... Probability Distribution: Definition, Formula & Example

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Chapter 20 / Lesson 11
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Learn the probability distribution definition for assessing possible outcomes of an event. Discover a probability distribution example and use it to make a table.