the dean of admissions in a large university has determined that the scores of the freshman class in a mathematics test are normally distributed with a mean of 86 and a standard deviation of 11. A sample of 50 students is selected at random from the entire freshman class. Based on this information, what is the standard deviation of the sampling distribution of the sample mean?
SEm = SD/√n
To find the standard deviation of the sampling distribution of the sample mean, you can use the formula:
Standard Deviation of the Sample Mean = Standard Deviation of the Population / Square Root of Sample Size
In this case, the standard deviation of the population is given as 11 and the sample size is 50. Plugging these values into the formula, we get:
Standard Deviation of the Sample Mean = 11 / √50
To simplify it further, you can calculate the square root of 50:
√50 ≈ 7.07
Now, divide the standard deviation of the population (11) by the square root of the sample size (7.07):
Standard Deviation of the Sample Mean = 11 / 7.07
Calculating this, we get:
Standard Deviation of the Sample Mean ≈ 1.56
Therefore, the standard deviation of the sampling distribution of the sample mean is approximately 1.56.