What is a linear combination of normal random variables?

This can be used to find probabilities when combining normal random variables

What is meant by the sample mean distribution?

• Suppose you have a population with distribution?X?and you take a random sample with?n?observations?X₁,?X₂, ...,?X_n
• The sample mean distribution is the distribution of the values of the sample mean

What does the sample mean distribution look like when?X?is normally distributed?

• If the population is normally distributed then the sample mean distribution is also normally distributedWorked Example

What is the Central Limit Theorem?

μ?is the mean of?X

• • σ2?is the variance of?X
  • n?is the size of the sample

Do I always need to use the Central Limit Theorem when working with the sample mean distribution?

• No – the Central Limit Theorem is not needed when the population is normally distributed