The s.d. of the sampling distribution of sample mean for the population with s.d. 0.5, population size 122 and sample size 22 is

The standard deviation (SD) of the sampling distribution of the sample mean, also known as the standard error (SE), can be calculated using the formula:

SE = SD / sqrt(n)

where:

• SD is the standard deviation of the population, and
• n is the sample size.

Given that the standard deviation of the population (SD) is 0.5 and the sample size (n) is 22, we can substitute these values into the formula:

SE = 0.5 / sqrt(22)

Now, calculate the square root of 22, which is approximately 4.69.

Then, divide 0.5 by 4.69 to get the standard error (SE), which is approximately 0.1066.

So, the standard deviation of the sampling distribution of the sample mean for the population with a standard deviation of 0.5, a population size of 122, and a sample size of 22 is approximately 0.1066.