Using the Central Limit Theorem, the branch manager can be 95% certain that the sample mean will fall within $1.034 of the mean.
<h3>What does the Central Limit Theorem state?</h3>- It states that the sampling distribution of sample means of size n has standard deviation
.
- 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:
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 brainly.com/question/24663213
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