Answered: Determine whether the graph shown could…

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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Determine whether the graph shown could represent a variable with a normal distribution. Explain your reasoning. If the graph appears to represent a normal distribution, estimate the mean and standard deviation.

Select the correct choice below and, if necessary, fill in the blanks to complete your choice.

a) The graph could represent a variable with a normal distribution because the curve is symmetric and bell-shaped. Its mean is approximately _______ and its standard deviation is approximately _______.

(Round to one decimal place as needed.)

b) The graph could not represent a variable with a normal distribution because the curve has two modes.

c) The graph could not represent a variable with a normal distribution because the graph is skewed to the right.

d) The graph could not represent a variable with a normal distribution because the curve crosses the x-axis.

e) The graph could not represent a variable with a normal distribution because the curve is constant.

f) The graph could not represent a variable with a normal distribution because the graph is skewed to the left.

The image depicts a bell-shaped curve, which appears symmetrical around its peak, indicating it might represent a normal distribution. The horizontal axis is labeled "x" and is marked with values ranging from 1 to 8. The peak of the curve is roughly centered around the value 4. This type of graph is commonly used in statistics to represent the distribution of data points. The smooth curve suggests that it is a continuous probability distribution, typically used to illustrate how data values are dispersed around a mean.

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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