I need an explanation on how to do these problems ### Understanding the Standard Normal DistributionThe image shows a bell curve that represents the Standard Normal Distribution. It is divided into sections labeled A to H, with corresponding areas shaded in different colors to indicate varying percentages of data within each section. Below is a detailed explanation of each part and its significance:#### Sections of the Standard Normal Distribution:- **A & H (Red Areas):** Represent the tails of the distribution, which are at the extremes and collectively account for 0.15% each.- **B & G (Yellow Areas):** Found just before the tails, each containing 2.35% of the data.- **C & F (Yellow Areas):** Adjacent to the central area, each section accounts for 13.5% of the data.- **D & E (Green Areas):** Compose the central part of the distribution, with each section containing 34% of the data.#### Important Statistical Markers:- **μ (Mu):** Represents the mean or average of the distribution, located at the center (0).- **σ (Sigma):** Refers to the standard deviation, which measures the amount of variation in the distribution. In this graph, sections are measured at intervals of σ (1σ, 2σ, 3σ).#### Key Percentage Breakdown:- **68%**: The area within 1 standard deviation (σ) of the mean, indicating where the majority of data points lie.- **95%**: The area within 2 standard deviations (2σ) of the mean, capturing a broader scope of data points.- **99.7%**: Almost all of the data, located within 3 standard deviations (3σ) of the mean.#### Z-Score Values:- **Z = -3 to 3:** Correspond to the standard deviations from the mean, with negative values on the left side and positive on the right.The interactive section at the bottom allows users to input the percentages of data in each section labeled A, B, and C.This diagram effectively visualizes the distribution of probabilities in a standard normal curve, which is critical for understanding concepts in statistics such as probability, standard deviation, and Z-scores. Sure! Here is a transcription and explanation of the content:---**Probability Problems for Adult American Male Height****Questions:**c. What is the probability of randomly selecting an adult American male who is less than 6ft (72 inches) tall?\[ P(X < 72) = \_\_\_\_ \]d. What is the probability of randomly selecting an adult American male who is between 70in and 73in tall?\[ P(70 < X < 73) = \_\_\_\_ \]e. **Use the table below to determine the following:**| Z-Score | Height ||---------|--------|| -3 | 61.5 || -2 | 64 || -1 | 66.5 || 0 | 69 || 1 | 71.5 || 2 | 74 || 3 | 76.5 |- **Question:** If there are approximately 152 million adult American men in the United States, how many of them do you expect to be between 69 and 71.5 inches tall?\[ \_\_\_\_ \] million American men.**Explanation of the Table:**The table shows Z-score values and their corresponding heights in inches for adult American males. Z-scores indicate how many standard deviations away a measurement is from the mean. The heights associated with the Z-scores range from 61.5 inches to 76.5 inches.**Intended Use:**This exercise is designed to help students apply their understanding of probability and the normal distribution to practical questions related to the heights of adult American males. Students will calculate probabilities using the information provided and the Z-score table, as well as estimate counts from a total population. --- This transcription and explanation should help students use this content effectively on an educational website.

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Answered: Express the amount of data in each…

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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Express the amount of data in each section of the Standard Normal Distribution as a percentage (%). DE G F H -30 -20 -1o lo За 68% 95% 99.7% Z: -3 -2 -1 0 1 2 3 A = B = C = 20 B- A-