Answer :
When a sample of size 25 is taken from a population with a mean of 120 and a standard deviation of 10,The expected distance between the sample mean and the population mean is 2.5.
The mean of a population is the average value of all the data points, while the standard deviation is a measure of how spread out the data points are. When a sample of size 25 is taken from a population with a mean of 120 and a standard deviation of 10, the expected distance between the sample mean and the population mean is 2.5. This is because the standard deviation of the sample mean is equal to the population standard deviation divided by the square root of the sample size. In this case, the standard deviation of the sample mean would be 10/5 = 2, and the expected distance between the sample mean and the population mean would be 2 x 2.5 = 2.5.
Standard deviation of the sample mean = Population standard deviation / √ Sample size
= 10 / √25
= 10 / 5
= 2
Expected distance between the sample mean and the population mean = 2 x 2.5
= 2.5
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