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?

A.
$45.38 and $46.42
B.
$44.35 and $47.45
C.
$44.87 and $46.93
D.
$45.85 and $45.95

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?

A. 
$45.38 and $46.42
B. 
$44.35 and $47.45
C. 
$44.87 and $46.93
D. 
$45.85 and $45.95

Gabbsmiles0 · Answer

By the Empirical Rule, within 2 standard deviations of the mean. So

45.90 - 2*0.5155 = $44.87

45.90 + 2*0.5155 = $46.93

Gabbsmiles0 · Answer

those would be the answers

DustinSettle · Answer

@gabbsmiles0 wrote:

those would be the answers

thank you

Gabbsmiles0 · Answer

@dustinsettle wrote:

@gabbsmiles0 wrote:

those would be the answers

thank you

your welcome

mhanifa · Answer

@gabbsmiles0 wrote:

By the Empirical Rule, within 2 standard deviations of the mean. So 45.90 - 2*0.5155 = $44.87 45.90 + 2*0.5155 = $46.93

Can you explain how did you get the standard deviation please?