Question

A population of values has a normal distribution with μ=6.5 and σ=17.6. A random sample of size n=239 is drawn.

a.What is the mean of the distribution of sample means?
μ¯x=
b. What is the standard deviation of the distribution of sample means? Round your answer to two decimal places.
σ¯x=

Answer 1

The mean of the distribution of sample means, μ¯x, is equal to the population mean, μ. The standard deviation of the distribution of sample means, σ¯x, is calculated by dividing the population standard deviation, σ, by the square root of the sample size, n.

Step-by-step explanation:

The mean of the distribution of sample means, μ¯x, is equal to the population mean, μ, which is 6.5.

The standard deviation of the distribution of sample means, σ¯x, is calculated by dividing the population standard deviation, σ, by the square root of the sample size, n, which is 239.

So, σ¯x = σ/√n = 17.6/√239 ≈ 1.14 (rounded to two decimal places).