Question

The branch manager of a clothing store is analyzing the average total bill of sale for his location. the national manager has communicated that the overall population mean is $45.90 with a standard deviation of $10.34. the branch manager has a sample of 400 total bills of sale for his location. by the central limit theorem, which interval can the branch manager be 95% certain that the sample mean will fall within?

Answer 1

Using the Central Limit Theorem, the branch manager can be 95% certain that the sample mean will fall within $1.034 of the mean.

What does the Central Limit Theorem state?

• It states that the sampling distribution of sample means of size n has standard deviation $s = \frac{\sigma}{\sqrt{n}}$.

• By the Empirical Rule, 95% of the sample means fall within 2 standard errors of the mean.

In this problem, we have that the standard deviation and the sample size are given as follows:

$\sigma = 10.34, n = 400$

Hence the standard error is given by:

[tex]s = \frac{10.34}{\sqrt{400}} = 0.517.

Two standard errors is represented by:

2 x 0.517 = $1.034.

Hence, the branch manager can be 95% certain that the sample mean will fall within $1.034 of the mean.

More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213

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