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
129316The Central Limit Theorem for Sample Means (Averages) · Exercise 1Medium
129318The Central Limit Theorem for Sample Means (Averages) · Exercise 5Medium
129319The Central Limit Theorem for Sample Means (Averages) · Exercise 7Medium
129321The Central Limit Theorem for Sample Means (Averages) · Exercise 9Medium
129323The Central Limit Theorem for Sample Means (Averages) · Exercise 11Medium
129325The Central Limit Theorem for Sample Means (Averages) · Exercise 13Medium
129327The Central Limit Theorem for Sample Means (Averages) · Exercise 15Medium
129366The Central Limit Theorem for Sums · Exercise 32Medium
129368The Central Limit Theorem for Sums · Exercise 34Medium
129417Using the Central Limit Theorem · Exercise 40Medium
129419Using the Central Limit Theorem · Exercise 42Medium
129421Using the Central Limit Theorem · Exercise 44Medium
129423Using the Central Limit Theorem · Exercise 46Medium
130513The Central Limit Theorem for Sample Means · Exercise 1Medium
130515The Central Limit Theorem for Sample Means · Exercise 3Medium
130517The Central Limit Theorem for Sample Means · Exercise 5Medium
130519The Central Limit Theorem for Sample Means · Exercise 7Medium
130521The Central Limit Theorem for Sample Means · Exercise 9Medium
130547The Central Limit Theorem for Proportions · Exercise 11Medium
131406The Central Limit Theorem for Sample Means (Averages) · Exercise 7Medium
131407The Central Limit Theorem for Sample Means (Averages) · Exercise 9Medium
131409The Central Limit Theorem for Sample Means (Averages) · Exercise 11Medium
131411The Central Limit Theorem for Sample Means (Averages) · Exercise 15Medium
131431The Central Limit Theorem for Sums (Optional) · Exercise 34Medium
131460Using the Central Limit Theorem · Exercise 40Medium
131462Using the Central Limit Theorem · Exercise 42Medium
131464Using the Central Limit Theorem · Exercise 44Medium
131466Using the Central Limit Theorem · Exercise 46Medium
129329The Central Limit Theorem for Sample Means (Averages) · Exercise 17Medium
129336The Central Limit Theorem for Sums · Exercise 1Medium
129338The Central Limit Theorem for Sums · Exercise 3Medium
129340The Central Limit Theorem for Sums · Exercise 5Medium
129342The Central Limit Theorem for Sums · Exercise 7Medium
129344The Central Limit Theorem for Sums · Exercise 9Medium
129346The Central Limit Theorem for Sums · Exercise 11Medium
129348The Central Limit Theorem for Sums · Exercise 13Medium
129350The Central Limit Theorem for Sums · Exercise 15Medium
129352The Central Limit Theorem for Sums · Exercise 17Medium
129355The Central Limit Theorem for Sums · Exercise 21Medium
129357The Central Limit Theorem for Sums · Exercise 23Medium
129359The Central Limit Theorem for Sums · Exercise 25Medium
129361The Central Limit Theorem for Sums · Exercise 27Medium
129363The Central Limit Theorem for Sums · Exercise 29Medium
129382Using the Central Limit Theorem · Exercise 1Medium
129384Using the Central Limit Theorem · Exercise 3Medium
129385Using the Central Limit Theorem · Exercise 5Medium
129386Using the Central Limit Theorem · Exercise 7Medium
129387Using the Central Limit Theorem · Exercise 9Medium
129388Using the Central Limit Theorem · Exercise 11Medium
129390Using the Central Limit Theorem · Exercise 13Medium
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