Normal Models and Sampling Distributions Review

AP Statistics Review Flashcards

Describe the characteristics of a normal model.

Unimodal, symmetric, mound-shaped, mean equals the median, continuous (approximates discrete distributions).

How do you represent the shape, center, and spread of a normal model?

N(μ, σ), where μ is the mean and σ is the standard deviation.

State the Empirical Rule (68%-95%-99.7% Rule).

Approximately 68% of the area is within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.

What is a z-score?

The number of standard deviations a data point is above or below the mean.

How do you calculate a z-score?

z = (x - μ) / σ, where x is the data point, μ is the mean, and σ is the standard deviation.

What is meant by Normalcdf Function

Normalcdf calculates the area under a normal curve between two z-score boundaries or the probability

What is meant by InvNorm Function

InvNorm (inverse Normal) takes an area of a normal and produces the X value

What is the Central Limit Theorem?

As the sample size n increases, the sampling distribution becomes more normal, regardless of the population's shape. If n ≥ 30, we assume normality.

When should you use the Central Limit Theorem?

When a question asks you to calculate a probability about an average or mean.

How does the standard deviation of the sampling distribution relate to the population standard deviation?

σx̄ = σ / √n, where σx̄ is the standard deviation of the sampling distribution, σ is the population standard deviation, and n is the sample size.

What is the formula for the Mean of the sampling distribution?

μ_x̄ = μ, The mean of the sampling distribution is the same as the mean of the population.