Question

A population of values has a normal distribution with μ=190.1μ=190.1 and σ=91.6σ=91.6. You intend to draw a random sample of size n=151n=151.

a) What is the mean of the distribution of sample means?
μ¯x=μx¯=

b) What is the standard deviation of the distribution of sample means?
(Report answer accurate to 2 decimal places.)
σ¯x=σx¯=

Answer 1

population of values has a normal distribution with μ =190.1  and σ = 91.6

random sample of size n = 151

a) What is the mean of the distribution of sample means?
μ¯x = ?

Sample mean is always equals to the population mean

μ¯x = μ =190.1

b) What is the standard deviation of the distribution of sample means?
(Report answer accurate to 2 decimal places.)
σ¯x = ?

Sample standard deviation σ¯x = σ/sqrt(n) = 91.6 /sqrt(151) =91.6* 0.0813788 = 7.4543 = 7.45

σ¯x = 7.45