EIP - Normal Distribution - Week 6

Question 1

Are normal distributions symmetrical?

Answer 1

Yes

Question 2

What can a normal distribution be completely described by (2) and why?

Answer 2

By its mean - a measure of central tendency

By its standard deviation - a measure of its variability

Question 3

What is the central limit theorem?

Answer 3

If random samples are taken from any distribution, then the distribution of sample means will be normal

Question 4

What happens when a small sample of the population is taken? What would repeated small sample distributions look like? How does a t-distribution fit in?

Answer 4

The sample distribution will not look normal
Repeated small sample distributions may not look like each other
The t-distribution allows you to see whether the difference between repeated small samples is real or due to random variation

Question 5

What happens to uncertainty in t-distributions the smaller the number of data points? what happens to the tails of the distribution?

Answer 5

The smaller the number of data points, the greater the uncertainty and the bigger the tails

Question 6

What happens to the tails of a distribution with smaller degrees of freedom?

Answer 6

They become wider