The Central Limit Theorem

Why the normal distribution keeps appearing.

12 problems · about 22 minutes · UNC-3.M

NameDate

Figure — use these to answer the problems

A symmetric bell shape. Sample means take this shape even when the population does not.

Low2

Mid-low7

Mid-high7

High2

Low2

Mid-low7

Mid-high7

High2

Figure 1

Straightforward practice. Get the method working first.

5 problems

Sigma 24 and n = 36. What is the standard error?
Answer
2
What does the Central Limit Theorem describe?
- The distribution of sample means, whatever the population shape.
- The distribution of individual data values.
The population is already normal, n = 5. Is the sampling distribution normal? 1 yes, 0 no.
Answer
The population is skewed, n = 50. Approximately normal? 1 yes, 0 no.
Answer
Does the theorem make the population normal? 1 yes, 0 no.
Answer

The same ideas with more to keep track of.

3 problems

Sigma 20, n = 100. Standard error?
Answer
Population mean 40. Where is the sampling distribution centred?
Answer
A more skewed population needs a larger or smaller n? 1 larger, 2 smaller.
Answer

Mixed problems. Work out what kind of question it is before you start.

4 problems

9
Which statements does the theorem support?
- Sample means become approximately normal for large n
- Normal-based inference works on skewed populations
- Individual data values become normal
- The population standard deviation shrinks
- Tick every box that applies.
Sigma 9, n = 9. Standard error?
Answer
The Guideline
What sample size is commonly cited as large enough for the theorem?
Answer
The Standard Error
Sigma 12 and n = 36. What is the standard error?
Answer