Let XX represent the full length of a certain species of newt. Assume that XX has a normal probability distribution with a mean of 75 inches and a standard deviation of 6.3 inches. You intend to measure a random sample of n=167 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.μx =σ¯x = The image displays a bell curve, which is characteristic of a normal distribution graph. ### Description of Graph:- **Bell Curve:** This symmetrical curve peaks at the mean, illustrating the distribution of data points where most values cluster around the central peak, tapering off equally on both sides. - **Horizontal Axis:** A number line spans across the bottom of the graph. The line is marked at regular intervals, with three highlighted sections along the axis. These sections likely represent specific ranges within the distribution.- **Vertical Axis:** While not explicitly labeled, the vertical axis represents the frequency or probability density of data points at each value along the horizontal axis.### Variables:- The graph includes two parameters: - **$\mu$ (Mu):** Representing the mean of the distribution, although the exact value is obscured. - **$\sigma$ (Sigma):** Representing the standard deviation, with the exact value also obscured.This graph is useful for visualizing how data points according to a normal distribution are spread in relation to the mean, with insight into variability provided by the standard deviation.

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Answered: Let XX represent the full length of a…

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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Let XX represent the full length of a certain species of newt. Assume that XX has a normal probability distribution with a mean of 75 inches and a standard deviation of 6.3 inches.

You intend to measure a random sample of n=167 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.

μx =

σ¯x =

The image displays a bell curve, which is characteristic of a normal distribution graph.

### Description of Graph:
- **Bell Curve:** This symmetrical curve peaks at the mean, illustrating the distribution of data points where most values cluster around the central peak, tapering off equally on both sides.
- **Horizontal Axis:** A number line spans across the bottom of the graph. The line is marked at regular intervals, with three highlighted sections along the axis. These sections likely represent specific ranges within the distribution.
- **Vertical Axis:** While not explicitly labeled, the vertical axis represents the frequency or probability density of data points at each value along the horizontal axis.

### Variables:
- The graph includes two parameters:
- **$\mu$ (Mu):** Representing the mean of the distribution, although the exact value is obscured.
- **$\sigma$ (Sigma):** Representing the standard deviation, with the exact value also obscured.

This graph is useful for visualizing how data points according to a normal distribution are spread in relation to the mean, with insight into variability provided by the standard deviation.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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