Below is a distribution of raw scores for Body Mass Index (BMI) for a population. The shape of the "sampling distribution of the mean" where N = 100 for this variable would be which shape? Hint: The picture below is not the sampling distribution of mean, but rather the population we use to create a sampling distribution. What shape are sampling distributions of the mean?Normally distributed.The shape is impossible to predict.Skewed in the opposite direction.Exactly the same. ### Understanding Body Mass Distribution in a PopulationThis histogram displays the body mass distribution of individuals in a given sample population. The x-axis represents the body mass in grams (g), ranging from 160 g to 230 g. The y-axis represents the number of individuals within each body mass interval.#### Detailed Analysis:- The histogram consists of vertical bars, each of which represents a specific range of body mass. The height of each bar indicates the number of individuals within that range.- The body mass intervals increase in increments of 5 grams, from 160 g to 230 g.- Most of the data points are concentrated between 160 g and 190 g, suggesting these are the most common body masses within the sample population.#### Key Observations:1. **Modal Class**: - The tallest bar is centered around the body mass range of 170-175 grams, indicating this is the most frequently occurring body mass range in the sample. Approximately 130 individuals fall into this category. 2. **Distribution Shape**: - The distribution is right-skewed (positively skewed), meaning there are more individuals with lower body masses and fewer individuals with higher body masses. 3. **Range & Spread**: - The spread of the data is from 160 g to 230 g, indicating the total range of body masses observed in the population is 70 grams. - The left side of the histogram has a steeper ascent compared to the gradual descent on the right side, confirming the right skew.4. **Frequency Count**: - There are fewer than 20 individuals at the extremes of the body mass range (both lower and upper), suggesting that extremely low or high body masses are less common. - There is a noticeable decline in the number of individuals as the body mass increases past 190 grams.This histogram helps in understanding the variability and commonality within the body mass of a population, which can be crucial for studies in health, nutrition, and biology. It is evident that there is a predominant body mass range, but also significant variation outside of that range.

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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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Below is a distribution of raw scores for Body Mass Index (BMI) for a population. The shape of the "sampling distribution of the mean" where N = 100 for this variable would be which shape? Hint: The picture below is not the sampling distribution of mean, but rather the population we use to create a sampling distribution. What shape are sampling distributions of the mean?

Normally distributed.

The shape is impossible to predict.

Skewed in the opposite direction.

Exactly the same.

### Understanding Body Mass Distribution in a Population

This histogram displays the body mass distribution of individuals in a given sample population. The x-axis represents the body mass in grams (g), ranging from 160 g to 230 g. The y-axis represents the number of individuals within each body mass interval.

#### Detailed Analysis:
- The histogram consists of vertical bars, each of which represents a specific range of body mass. The height of each bar indicates the number of individuals within that range.
- The body mass intervals increase in increments of 5 grams, from 160 g to 230 g.
- Most of the data points are concentrated between 160 g and 190 g, suggesting these are the most common body masses within the sample population.

#### Key Observations:
1. **Modal Class**:
- The tallest bar is centered around the body mass range of 170-175 grams, indicating this is the most frequently occurring body mass range in the sample. Approximately 130 individuals fall into this category.

2. **Distribution Shape**:
- The distribution is right-skewed (positively skewed), meaning there are more individuals with lower body masses and fewer individuals with higher body masses.

3. **Range & Spread**:
- The spread of the data is from 160 g to 230 g, indicating the total range of body masses observed in the population is 70 grams.
- The left side of the histogram has a steeper ascent compared to the gradual descent on the right side, confirming the right skew.

4. **Frequency Count**:
- There are fewer than 20 individuals at the extremes of the body mass range (both lower and upper), suggesting that extremely low or high body masses are less common.
- There is a noticeable decline in the number of individuals as the body mass increases past 190 grams.

This histogram helps in understanding the variability and commonality within the body mass of a population, which can be crucial for studies in health, nutrition, and biology. It is evident that there is a predominant body mass range, but also significant variation outside of that range.

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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