Questions: Fill in the blank. The standard deviation of the distribution of sample means is - The standard deviation of the distribution of sample means is μ σ. μ/√n σ/√n

Solution Steps

To find the standard deviation of the distribution of sample means, we use the formula for the standard error of the mean, which is the population standard deviation divided by the square root of the sample size.

The standard deviation of the distribution of sample means, also known as the standard error of the mean, is calculated using the formula: \[ SE = \frac{\sigma}{\sqrt{n}} \] where \( \sigma \) is the population standard deviation and \( n \) is the sample size.

Given:

• \( \sigma = 10 \)
• \( n = 25 \)

Substituting these values into the formula gives: \[ SE = \frac{10}{\sqrt{25}} \]

Calculating \( \sqrt{25} \): \[ \sqrt{25} = 5 \] Now substituting back: \[ SE = \frac{10}{5} = 2.0 \]

Final Answer