any Aplia problems use the following Distributions tool. You can use this tool to retrieve the information that you would get from a distributions table. The advantage of the tool is that it allows you to see in two dimensions how changing parameters, such as the z-score, will affect the resulting probabilities. Use the tool to complete the following table. z Body Tail Mean to z z Body Tail Mean to z 0.25 0.5987 0.4013 0.0987 1.55 0.9394 0.0606 0.4394 0.75 2.15 0.9842 0.0158 0.4842 1.10 0.8643 0.1357 0.3643 2.65 1.30 0.9032 0.0968 0.4032 2.80 0.9974 0.0026 0.4974 To find the probability of a z-score, position the orange line at the appropriate z-score on the horizontal axis. The areas under the standard normal curve to the left and right of the vertical line are displayed in blue and orange, respectively. (Hint: The standard normal distribution is symmetrical about the mean, the area under the curve to the left (and right) of the mean is 0.5. Therefore, the area that corresponds with Mean to z is computed as Larger Portion (Body or Tail) – 0.5.) Standard Normal Distribution Mean = 0.0 Standard Deviation = 1.0 -3.00-2.50-2.00-1.50-1.00-0.500.000.501.001.502.002.503.00z.5000.50000.000 Grade It Now Save & Continue

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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Many Aplia problems use the following Distributions tool. You can use this tool to retrieve the information that you would get from a distributions table. The advantage of the tool is that it allows you to see in two dimensions how changing parameters, such as the z-score, will affect the resulting probabilities.

Use the tool to complete the following table.


z	Body	Tail	Mean to z	z	Body	Tail	Mean to z
0.25	0.5987	0.4013	0.0987	1.55	0.9394	0.0606	0.4394
0.75				2.15	0.9842	0.0158	0.4842
1.10	0.8643	0.1357	0.3643	2.65
1.30	0.9032	0.0968	0.4032	2.80	0.9974	0.0026	0.4974

To find the probability of a z-score, position the orange line at the appropriate z-score on the horizontal axis. The areas under the standard normal curve to the left and right of the vertical line are displayed in blue and orange, respectively.

(Hint: The standard normal distribution is symmetrical about the mean, the area under the curve to the left (and right) of the mean is 0.5. Therefore, the area that corresponds with Mean to z is computed as Larger Portion (Body or Tail) – 0.5.)

Standard Normal Distribution

Mean = 0.0

Standard Deviation = 1.0

-3.00-2.50-2.00-1.50-1.00-0.500.000.501.001.502.002.503.00z.5000.50000.000

Grade It Now

Save & Continue

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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