AP Statistics 4.2.A Describing t-Distributions

Practise describing t-distributions by comparing their symmetry and tails with the normal model, tracking degrees of freedom, and identifying the correct t-statistic.

Exam points

Recognise t-distributions as symmetric and heavier-tailed than the standard normal distribution.
Explain how increasing degrees of freedom makes a t-distribution approach the normal model.
Use n minus one degrees of freedom when standardising a sample mean with the sample standard deviation.

[Maximum number: 1]

A population is normally distributed with mean 25. Consider all samples of size 10 . The variable $\frac{\bar{x}-25}{\frac{s}{\sqrt{10}}}$

has a normal distribution.

has a t-distribution with d f=10.

has a t-distribution with d f=9.

has either a normal or a t-distribution depending on the characteristics of the population standard deviation.

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4.2.A—Describe t-distributions question 1