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...

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)?

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