A population of values has a normal distribution with μ = 52.7 and σ = 72 . you intend to draw a random sample of size n = 227 . 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 =

Respuesta :

The standard deviation of a particular sample is equal to the standard deviation divided by the square root of the sample size.  That is,
[tex]\sigma_x=\frac{\sigma}{\sqrt n}[/tex]
The mean of a particular sample is equal to the mean of the set the sample was taken from.  That is,
[tex]\mu_x=\mu[/tex]
[tex]\text{In your case, }\sigma_x=\frac{72}{\sqrt{227}}\approx 4.78\text{ and }\mu_x=52.7[/tex]