Question

.) A population of values has a normal distribution with μ=27.5 and σ=71.5. You intend to draw a random sample of size n=180.

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

Answer: a) 27.5, b) 5.33.

Explanation:

Since we have given that

`\mu =27.5\\\\\sigma =71.5`

and n = 180

We need to calculate the sample mean and sample standard deviation.

So, the mean of the distribution of sample means is

`\mu = \mu_x=27.5`

The standard deviation of the distribution of sample means is

`s=(\sigma)/(√(n))=(71.5)/(√(180))=5.329=5.33`

Hence, a) 27.5, b) 5.33.