A population of values has a normal distribution with μ = 35.8 and σ = 48.2 . You intend to draw a random sample of size n = 102

Question

What is the mean of the distribution of sample means? 

μ¯x= 

What is the standard deviation of the distribution of sample means? 

(Report answer accurate to 2 decimal places.) 

σ¯x=

Answer 1

Hi Salma,

When you have large n, we can assume that:

mu_x-bar=mu=35.8

Now, some books call “large n” 30, some say 50, but 102 is certainly enough, so:

mu_x-bar=35.8

Standard deviation of sample mean has its own name and its own formula. It is called the standard error, and the formula is:

SE=sigma/sqrt(n)

Breaking this down:

SE=standard error

sigma=standard deviation

n=sample size

For our problem:

SE=what we’re looking for

sigma=48.2

n=102

Thus:

SE=48.2/sqrt(102)

SE=4.77

I hope this helps.