Suppose a random variable X is normally distributed with mean 100 and standard deviation 15

suppose a random variable X is normally distributed with mean 100 and standard deviation 15
Would a sample mean of 105 or higher be more likely from a sample of size n=10 or n=20? Explain your answer?

Jasmine -

Answer is n = 10

The smaller the sample size, the larger will be the standard error.

standard error = 15 / sqrt (n)

So, the larger the standard error, the greater chance the sample mean will fall farther from the true population mean of 100.

Hope that helps