Let X represent the full length of a certain species of newt. Assume that X has a normal probability distribution with mean 185.3 inches and standard deviation 5.7 inches. You intend to measure a random sample of n = 244 newts. The bell curve below represents the distibution of these sample means. The scale on the horizontal axis is the standard error of the sampling distribution. Complete the indicated boxes, correct to two decimal places. 「ェ =
Let X represent the full length of a certain species of newt. Assume that X has a normal probability distribution with mean 185.3 inches and standard deviation 5.7 inches. You intend to measure a random sample of n = 244 newts. The bell curve below represents the distibution of these sample means. The scale on the horizontal axis is the standard error of the sampling distribution. Complete the indicated boxes, correct to two decimal places. 「ェ =
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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![**Sampling Distribution of the Mean for Newt Lengths**
Let \( X \) represent the full length of a certain species of newt. Assume that \( X \) has a normal probability distribution with mean 185.3 inches and standard deviation 5.7 inches.
You intend to measure a random sample of \( n = 244 \) newts. The bell curve below represents the distribution of these sample means. The scale on the horizontal axis is the standard error of the sampling distribution. Complete the indicated boxes, correct to two decimal places.
\[
\mu_{\bar{X}} = \text{\underline{\ \ \ \ \ \ \ \ }}
\]
\[
\sigma_{\bar{X}} = \text{\underline{\ \ \ \ \ \ \ \ }}
\]
**Explanation of the Bell Curve Diagram:**
The bell curve (normal distribution) shown represents the sampling distribution of the sample mean lengths of newts. The center of the curve (the peak) indicates the mean of the sample means, denoted as \( \mu_{\bar{X}} \). The width of the curve is determined by the standard error, denoted as \( \sigma_{\bar{X}} \).
To complete the diagram:
1. **\( \mu_{\bar{X}} \)**: This represents the mean of the sample means, which is equal to the population mean \( \mu = 185.3 \) inches.
2. **\( \sigma_{\bar{X}} \)**: This represents the standard error of the sample mean, calculated using the formula \( \sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}} \), where \( \sigma = 5.7 \) inches and \( n = 244 \).
\[
\mu_{\bar{X}} = 185.30
\]
\[
\sigma_{\bar{X}} = \frac{5.7}{\sqrt{244}} \approx \frac{5.7}{15.62} \approx 0.36
\]
Therefore, correctly rounded to two decimal places, we have:
\[
\mu_{\bar{X}} = 185.30
\]
\[
\sigma_{\bar{X}} = 0.36
\]
Fill these values into the corresponding boxes on the diagram.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb19bde89-b2cc-45cf-a738-49c577841102%2F44906eb4-0326-455e-8ea6-efaecd669a45%2Fv0z2hux_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Sampling Distribution of the Mean for Newt Lengths**
Let \( X \) represent the full length of a certain species of newt. Assume that \( X \) has a normal probability distribution with mean 185.3 inches and standard deviation 5.7 inches.
You intend to measure a random sample of \( n = 244 \) newts. The bell curve below represents the distribution of these sample means. The scale on the horizontal axis is the standard error of the sampling distribution. Complete the indicated boxes, correct to two decimal places.
\[
\mu_{\bar{X}} = \text{\underline{\ \ \ \ \ \ \ \ }}
\]
\[
\sigma_{\bar{X}} = \text{\underline{\ \ \ \ \ \ \ \ }}
\]
**Explanation of the Bell Curve Diagram:**
The bell curve (normal distribution) shown represents the sampling distribution of the sample mean lengths of newts. The center of the curve (the peak) indicates the mean of the sample means, denoted as \( \mu_{\bar{X}} \). The width of the curve is determined by the standard error, denoted as \( \sigma_{\bar{X}} \).
To complete the diagram:
1. **\( \mu_{\bar{X}} \)**: This represents the mean of the sample means, which is equal to the population mean \( \mu = 185.3 \) inches.
2. **\( \sigma_{\bar{X}} \)**: This represents the standard error of the sample mean, calculated using the formula \( \sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}} \), where \( \sigma = 5.7 \) inches and \( n = 244 \).
\[
\mu_{\bar{X}} = 185.30
\]
\[
\sigma_{\bar{X}} = \frac{5.7}{\sqrt{244}} \approx \frac{5.7}{15.62} \approx 0.36
\]
Therefore, correctly rounded to two decimal places, we have:
\[
\mu_{\bar{X}} = 185.30
\]
\[
\sigma_{\bar{X}} = 0.36
\]
Fill these values into the corresponding boxes on the diagram.
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