Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with u = 118.5 ft and o = 34 ft. You intend to measure a random sample of n = 67 trees. What is the mean of the distribution of sample means? 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.)

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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**Problem Description**

Let \( X \) represent the full height of a certain species of tree. Assume that \( X \) has a normal probability distribution with a mean (\( \mu \)) of 118.5 ft and a standard deviation (\( \sigma \)) of 34 ft.

You intend to measure a random sample of \( n = 67 \) trees.

**Questions**

1. What is the mean of the distribution of sample means?

   \( \mu_{\bar{x}} = \)

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.)

   \( \sigma_{\bar{x}} = \)
Transcribed Image Text:**Problem Description** Let \( X \) represent the full height of a certain species of tree. Assume that \( X \) has a normal probability distribution with a mean (\( \mu \)) of 118.5 ft and a standard deviation (\( \sigma \)) of 34 ft. You intend to measure a random sample of \( n = 67 \) trees. **Questions** 1. What is the mean of the distribution of sample means? \( \mu_{\bar{x}} = \) 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.) \( \sigma_{\bar{x}} = \)
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