A random sample of size 50 is taken from a large population with mean 𝝁 = 𝟏𝟔𝟎 and standard deviation 𝝈 = 𝟏𝟖.

Question

A random sample of size 50 is taken from a large population with mean 𝝁 = 𝟏𝟔𝟎 and standard deviation 𝝈 = 𝟏𝟖. What is the mean of the sampling distribution of the sample means? (is 160 the correct answer?)

What is the standard error of the sampling distribution of the sample means? ( is 2.55 the correct answer?)

Answer 1

For the first part of your question, is 160 the correct mean of sampling distrobution... yes 160 is the correct mean. If you take 50 samples at a time, and do this repeatedly, the average of all those samples should be extremely close to the original average, in this case 160.

For the second part... is 2.55 the correct standard devation? The answer again is yes! To find the std devation of sampling distrobution, you simply take σ/sqrt(n) = 18/sqrt(50) = 2.545584412

Great work, correct on both counts!