5.4 Sampling Distributions and the Central Limit

Question 1

Sampling distribution

Answer 1

The probability distribution of a sample statistics that is formed when random samples of size are repeatedly taken from a population.

Question 2

Properties of Sampling Distributions of Sample Mean

Answer 2

1. The mean of the sample means μx̄, is equal to the population mean μ x̄ = μ
2. The standard deviation of the sample means, σ x̄ , is equal to the population standard deviation, σ, divided by the square root of the sample size, n.
   σ x̄ = σ√n
   - called the standard error of the mean.

Question 3

Probability and the Central Limit Theorem

Answer 3

• To transform x̄ to a z-score
  z = value - mean / standard error