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Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with u :171.7 ft ando = 91.5 ft. You intend to measure a random sample of n = 242 trees. What is the mean of the distribution of sample means? ft What is the standard deviation of the distribution of sample means (i.e., the standard error in estimating the mean)? (Report answer accurate to 2 decimal places.) ft

Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with u :171.7 ft ando = 91.5 ft. You intend to measure a random sample of n = 242 trees. What is the mean of the distribution of sample means? ft What is the standard deviation of the distribution of sample means (i.e., the standard error in estimating the mean)? (Report answer accurate to 2 decimal places.) ft

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Transcription for Educational Website** --- Let \( X \) represent the full height of a certain species of tree. Assume that \( X \) has a normal probability distribution with \( \mu = 171.7 \) ft and \( \sigma = 91.5 \) ft. You intend to measure a random sample of \( n = 242 \) trees. 1. What is the mean of the distribution of sample means? \( \mu_{\bar{x}} = \) ______ ft 2. What is the standard deviation of the distribution of sample means (i.e., the standard error in estimating the mean)? (Report answer accurate to 2 decimal places.) \( \sigma_{\bar{x}} = \) ______ ft [Check Answer] --- **Explanation:** This exercise is an application of statistical concepts related to the sampling distribution of the mean. The distribution of sample means will have the same mean as the population mean, \( \mu \), and its standard deviation (standard error) is calculated using the formula \( \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \), where \( n \) is the sample size.
Transcribed Image Text:**Transcription for Educational Website** --- Let \( X \) represent the full height of a certain species of tree. Assume that \( X \) has a normal probability distribution with \( \mu = 171.7 \) ft and \( \sigma = 91.5 \) ft. You intend to measure a random sample of \( n = 242 \) trees. 1. What is the mean of the distribution of sample means? \( \mu_{\bar{x}} = \) ______ ft 2. What is the standard deviation of the distribution of sample means (i.e., the standard error in estimating the mean)? (Report answer accurate to 2 decimal places.) \( \sigma_{\bar{x}} = \) ______ ft [Check Answer] --- **Explanation:** This exercise is an application of statistical concepts related to the sampling distribution of the mean. The distribution of sample means will have the same mean as the population mean, \( \mu \), and its standard deviation (standard error) is calculated using the formula \( \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \), where \( n \) is the sample size.
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