Explanation

The standard error of the mean (SEM) is calculated using the formula:

$SEM = \frac{s}{\sqrt{n}}$

Where:

• $s$ = sample standard deviation = 3.5
• $n$ = sample size = 30

Substituting the values:

$SEM = \frac{3.5}{\sqrt{30}} = \frac{3.5}{5.477} ≈ 0.639$

This value (0.639) is closest to 0.64 among the given options.

Key points:

• Standard error measures the precision of the sample mean as an estimate of the population mean
• It decreases as sample size increases
• The formula assumes the sample is representative of the population
• In this case, with n=30, we get SEM ≈ 0.64