The per capita energy consumption level (in kilowatt-hours) in a certain country for a recent year can be approximated by a normal distribution, as shown in the figure. (a) What consumption level represents the 9th percentile?(b) What consumption level represents the 19th percentile?(c) What consumption level represents the third quartile?(a) The consumption level that represents the9thpercentile isenter your response herekilowatt-hours.(Round to the nearest integer as needed.)(b) The consumption level that represents the19thpercentile isenter your response herekilowatt-hours.(Round to the nearest integer as needed.)(c) The consumption level that represents thethirdquartile isenter your response herekilowatt-hours.(Round to the nearest integer as needed.) ### Normal Distribution of Kilowatt-HoursThe graph above represents a normal distribution of kilowatt-hours (kWh) used. Specifically, this distribution is centered around the mean \( \mu = 2321 \) kWh and has a standard deviation \( \sigma = 570.9 \) kWh.- **Horizontal Axis (x-axis):** The x-axis represents the kilowatt-hours used, ranging from 321 kWh to 4321 kWh. - Major ticks on the x-axis: 321 kWh, 2321 kWh, and 4321 kWh.- **Vertical Axis (y-axis):** The y-axis represents the frequency or probability density of the kilowatt-hour usage.**Mean ( \( \mu \) ):**- The mean value, \( \mu \), is indicated at 2321 kWh. This is the peak of the bell-shaped curve, signifying the average kilowatt-hour usage.**Standard Deviation ( \( \sigma \) ):**- The standard deviation, \( \sigma \), is 570.9 kWh. This measurement provides insight into the dispersion or spread of the usage data around the mean. Smaller standard deviations indicate that the data points are closer to the mean, while larger standard deviations indicate that the data points are spread out over a larger range of values.The bell curve illustrates that most of the kilowatt-hour usages are clustered around the mean (2321 kWh), with fewer occurrences as we move away from the mean. In a normal distribution, about 68% of the data falls within one standard deviation of the mean, about 95% within two standard deviations, and nearly all (99.7%) within three standard deviations.This graph is an essential tool for understanding the variability and distribution of electricity consumption, useful for energy management, and forecasting usage patterns.

The question is about normal distribution Given : From given normal curve Mean of per capita energy…

Answered: The per capita energy consumption…

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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Question

The per capita energy consumption level (in kilowatt-hours) in a certain country for a recent year can be approximated by a normal distribution, as shown in the figure.
(a) What consumption level represents the 9th percentile?
(b) What consumption level represents the 19th percentile?
(c) What consumption level represents the third quartile?

(a) The consumption level that represents the
9th
percentile is
enter your response here
kilowatt-hours.
(Round to the nearest integer as needed.)

(b) The consumption level that represents the
19th
percentile is
enter your response here
kilowatt-hours.
(Round to the nearest integer as needed.)

(c) The consumption level that represents the
third
quartile is
enter your response here
kilowatt-hours.
(Round to the nearest integer as needed.)

### Normal Distribution of Kilowatt-Hours

The graph above represents a normal distribution of kilowatt-hours (kWh) used. Specifically, this distribution is centered around the mean \( \mu = 2321 \) kWh and has a standard deviation \( \sigma = 570.9 \) kWh.

- **Horizontal Axis (x-axis):** The x-axis represents the kilowatt-hours used, ranging from 321 kWh to 4321 kWh.
- Major ticks on the x-axis: 321 kWh, 2321 kWh, and 4321 kWh.
- **Vertical Axis (y-axis):** The y-axis represents the frequency or probability density of the kilowatt-hour usage.

**Mean ( \( \mu \) ):**
- The mean value, \( \mu \), is indicated at 2321 kWh. This is the peak of the bell-shaped curve, signifying the average kilowatt-hour usage.

**Standard Deviation ( \( \sigma \) ):**
- The standard deviation, \( \sigma \), is 570.9 kWh. This measurement provides insight into the dispersion or spread of the usage data around the mean. Smaller standard deviations indicate that the data points are closer to the mean, while larger standard deviations indicate that the data points are spread out over a larger range of values.

The bell curve illustrates that most of the kilowatt-hour usages are clustered around the mean (2321 kWh), with fewer occurrences as we move away from the mean. In a normal distribution, about 68% of the data falls within one standard deviation of the mean, about 95% within two standard deviations, and nearly all (99.7%) within three standard deviations.

This graph is an essential tool for understanding the variability and distribution of electricity consumption, useful for energy management, and forecasting usage patterns.

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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