### Understanding Normal Distribution through an Example of Adult Spider Carapace LengthsA study finds that the carapace length of an adult spider is normally distributed with the following parameters:- Mean (µ): 14.27 mm- Standard Deviation (σ): 1.25 mmLet $ x $ denote carapace length for an adult spider.To understand the distribution and specific characteristics of this dataset, several statistical analyses and representations can be performed.#### a. Identify and Sketch the Distribution of ZTo comprehend the distribution, you need to identify the correct graphical representation. The options provided are typically for understanding the shape and spread of a normal distribution.(Graph options are usually labeled as A, B, C, etc., which represent possible shapes of the normal distribution curve).#### b. Z-Scores Corresponding to Specific Percentages1. **Percentage of Adult Spiders with Carapace Lengths between 12 mm and 13 mm** To find the percentage of carapace lengths between 12 mm and 13 mm, calculate the Z-scores for these values and then find the corresponding area under the standard normal curve: - Z-score for x = 12 mm: \[ Z = \frac{12 - 14.27}{1.25} \approx -1.82 \] - Z-score for x = 13 mm: \[ Z = \frac{13 - 14.27}{1.25} \approx -1.02 \] (These need to be rounded to two decimal places.)#### c. Percentage of Carapace Lengths Exceeding 15 mm To find the percentage of adult spiders with carapace lengths exceeding 15 mm: - Calculate the Z-score for 15 mm: \[ Z = \frac{15 - 14.27}{1.25} \approx 0.58 \] This Z-score can be converted to a percentage by finding the area to the right of this value under the standard normal distribution curve.### Visual Representation and DetailsAccompanying these calculations are graphs that illustrate the normal distribution curve, the area corresponding to certain Z-scores, and the specific intervals.- **Graph A**: Typically depicts a standard normal distribution.- **Graph B**: Focuses on smaller region or specific plot representation.- **Graph

The mean is 14.27 and the standard deviation is 1.25.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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