AP Statistics 4.1.B Conditions for Sample Mean Distributions

Practise justifying sample-mean inference by checking random sampling and using a large sample to obtain an approximately normal distribution from a skewed population.

Exam points

Require random sampling before generalising a sample mean or building a population-mean interval.
Use a large sample to justify an approximately normal sampling distribution from a skewed population.

[Maximum number: 1]

The sampling distribution of the sample mean is close to the normal distribution

only if both the original population has a normal distribution and n is large.

if the standard deviation of the original population is known.

if n is large, no matter what the distribution of the original population.

only if the original population is not badly skewed and does not have outliers.

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4.1.B—Justify the appropriateness of conditions for the sampling distribution of a sample mean question 1