2. Need help please **Why is the standard deviation of the distribution of sample means smaller than the standard deviation of the population from which it came?**Select all that apply.- ☑️ According to the central limit theorem, we divide the population standard deviation \( \sigma \) by the square root of the sample size \( n \), so as \( n \) gets bigger the quotient gets smaller.- ⬜ Since we are only graphing the averages of the samples, extremes like the minimum and maximum of each sample are not present, making the standard deviation of the sample means smaller than the standard deviation of the population.- ⬜ The standard deviation of the distribution of sample means is smaller than the standard deviation of the population because a sample is always small than the population.

Central Limit Theorem: Central limit theorem states that the sampling distribution of the sample mean follows an approximately normal distribution this is possible only when the sample size is large (n>30) no matter what is the shape of the population distribution.The mean of sampling distribution of the sample mean is equal to the population mean that is The standard deviation of the sampling distribution of the sample mean is ratio of standard deviation divided by square root of sample size The standard deviation of the distribution of sample mean is smaller than the population standard deviation because we divide the population standard deviation by the square root of sample size so as n gets bigger the quotient gets smaller. According to the Central limit theorem we divide the population standard deviation by the square root of sample size so as n gets bigger the quotient gets smaller. Option A is correct According to the Central limit theorem we divide the population standard deviation by the square root of sample size so as n gets bigger the quotient gets smaller.

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Probability

Why is the standard deviation of the distribution of sample means smaller than the standard deviation of the population from which it came? Select all that apply.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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