Sampling Distribution

Central Limit Theorem

Central Limit Theorem

With independent observations with mean and variance , and , sample mean is approximated by a normal distribution.

Sampling Distribution of Sample Proportion

With a random sample of size which has calculated as:

if , distribution of is approximated by

Sampling Distribution of Sample Mean

When the population distribution is normally distributed then,

• the histogram of has normal distribution
• the variability of bell-shaped gets less as increases
• bell shapes are all centered at population mean
• sampling distribution of depends on

When population distribution is not normally distributed then,

• if , is approximately normally distributed

Note that:

• histograms of is still close to bell-shaped
• variability of the bell-shape gets less as we increase
• bell-shapes centered at population mean
• sampling distribution of depends on