Lemma

Statistics · Chapter 5 of 10

Sampling distributions

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The sampling distribution of the sample mean describes how varies across all possible samples of size from a population. Its center is the population mean , and its spread is the standard error . If the population is normal, or if is large enough for the Central Limit Theorem, is approximately normally distributed. To find probabilities or percentiles, convert to a -score using , then use the standard normal table or technology.

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#TitleDifficulty
129307The Central Limit Theorem for Sample Means (Averages) · Example 1Easy
129308The Central Limit Theorem for Sample Means (Averages) · Example 2Easy
129310The Central Limit Theorem for Sample Means (Averages) · Example 3Easy
129312The Central Limit Theorem for Sample Means (Averages) · Example 4Easy
129314The Central Limit Theorem for Sample Means (Averages) · Example 5Easy
129332The Central Limit Theorem for Sums · Example 2Easy
129334The Central Limit Theorem for Sums · Example 3Easy
129377Using the Central Limit Theorem · Example 7Easy
129379Using the Central Limit Theorem · Example 8Easy
130550Finite Population Correction Factor · Example 1Easy
130551Finite Population Correction Factor · Try It 1Easy
130552Finite Population Correction Factor · Example 2Easy
130553Finite Population Correction Factor · Try It 2Easy
131401The Central Limit Theorem for Sample Means (Averages) · Example 3Easy
131402The Central Limit Theorem for Sample Means (Averages) · Try It 2Easy
131403The Central Limit Theorem for Sample Means (Averages) · Example 4Easy
131404The Central Limit Theorem for Sample Means (Averages) · Try It 3Easy
131405The Central Limit Theorem for Sample Means (Averages) · Example 5Easy
131414The Central Limit Theorem for Sums (Optional) · Example 2Easy
131415The Central Limit Theorem for Sums (Optional) · Try It 2Easy
131416The Central Limit Theorem for Sums (Optional) · Example 3Easy
131417The Central Limit Theorem for Sums (Optional) · Try It 3Easy
131433Using the Central Limit Theorem · Example 7Easy
131434Using the Central Limit Theorem · Try It 3Easy
131435Using the Central Limit Theorem · Example 8Easy
131436Using the Central Limit Theorem · Try It 4Easy
131413The Central Limit Theorem for Sums (Optional) · Try It 1Easy
131437Using the Central Limit Theorem · Try It 5Easy
129309The Central Limit Theorem for Sample Means (Averages) · Try It 1Easy
129311The Central Limit Theorem for Sample Means (Averages) · Try It 2Easy
129313The Central Limit Theorem for Sample Means (Averages) · Try It 3Easy
129315The Central Limit Theorem for Sample Means (Averages) · Try It 4Easy
129330The Central Limit Theorem for Sums · Example 1Easy
129331The Central Limit Theorem for Sums · Try It 1Easy
129333The Central Limit Theorem for Sums · Try It 2Easy
129335The Central Limit Theorem for Sums · Try It 3Easy
129369Using the Central Limit Theorem · Example 1Easy
129370Using the Central Limit Theorem · Example 2Easy
129371Using the Central Limit Theorem · Example 3Easy
129372Using the Central Limit Theorem · Example 4Easy
129373Using the Central Limit Theorem · Try It 1Easy
129374Using the Central Limit Theorem · Example 5Easy
129375Using the Central Limit Theorem · Example 6Easy
129376Using the Central Limit Theorem · Try It 2Easy
129378Using the Central Limit Theorem · Try It 3Easy
129380Using the Central Limit Theorem · Try It 4Easy
129381Using the Central Limit Theorem · Try It 5Easy
131432Using the Central Limit Theorem · Example 6Easy