QUESTION 6
sigma xbar 3 :
Suppose a sample of 114 healthy adult human body temperatures is taken from a population with a standard deviation of 0.5 degrees Fahrenheit. What would be the standard error of the sample mean?
Round to the nearest thousandth

Step 1 ：Given a sample of 114 healthy adult human body temperatures taken from a population with a standard deviation of 0.5 degrees Fahrenheit.

Step 2 ：We are asked to find the standard error of the sample mean.

Step 3 ：The standard error of the sample mean can be calculated using the formula: \(SE = \frac{\sigma}{\sqrt{n}}\), where \(\sigma\) is the standard deviation of the population and \(n\) is the size of the sample.

Step 4 ：In this case, \(\sigma = 0.5\) degrees Fahrenheit and \(n = 114\).

Step 5 ：Substituting the given values into the formula, we get \(SE = \frac{0.5}{\sqrt{114}} = 0.0468292905790847\).

Step 6 ：Rounding to the nearest thousandth, we get \(SE = 0.047\).

Step 7 ：Final Answer: The standard error of the sample mean is \(\boxed{0.047}\).