Question

1.) A population of values has a normal distribution with μ=33.7μ=33.7 and σ=19.7σ=19.7. You intend to draw a random sample of size n=113n=113.
a.))) What is the mean of the distribution of sample means?

b.))) What is the standard deviation of the distribution of sample means?

2.) A population has parameters μ=143.4μ=143.4 and σ=49.4σ=49.4. You intend to draw a random sample of size n=156n=156.
a.))) What is the mean of the distribution of sample means?

b.))) What is the standard deviation of the distribution of sample means?

3.) A population of values has a normal distribution with μ=109.1μ=109.1 and σ=62σ=62. You intend to draw a random sample of size n=143n=143.
a.))) What is the mean of the distribution of sample means?

b.))) What is the standard deviation of the distribution of sample means (i.e. the standard error)?

Answer 1

Here we are going to use Central limit theorem, which says if n>30, sampling distribution tends to normal even if the population distribution is not normal

1. Here n=113.

a. So sample mean is normally distributed with mean value

b. Standard deviation of sample mean is

2. Here n=156.

a. So sample mean is normally distributed with mean value

b. Standard deviation of sample mean is

3. Here n=143.

a. So sample mean is normally distributed with mean value

b. Standard deviation of sample mean is