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(b) Sketch the region corresponding to the statement P(z < c) = 0.2. Shade: Left of a value +++++++++++ -3 -4 Click and drag the arrows to adjust the values. -2 -1 0 1 ||||||||||| 3 2 4

(b) Sketch the region corresponding to the statement P(z < c) = 0.2. Shade: Left of a value +++++++++++ -3 -4 Click and drag the arrows to adjust the values. -2 -1 0 1 ||||||||||| 3 2 4

MATLAB: An Introduction with Applications
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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**(b) Sketch the region corresponding to the statement \( P(z < c) = 0.2 \).** **Shade:** Left of a value. Click and drag the arrows to adjust the values. **Explanation of the Graph:** The image depicts a standard normal distribution curve, which is a bell-shaped curve symmetric around zero. The x-axis is labeled with values ranging from -4 to 4. The area under the curve represents probabilities. In this graph, a region to the left of a value (denoted by \( c \)) is shaded in blue, indicating the probability. The blue shaded area corresponds to \( P(z < c) = 0.2 \), meaning that there is a 20% probability that the random variable \( z \) takes on a value less than \( c \). The shaded region starts at the far left and ends at approximately \( z = -0.84 \), which is marked with an arrow. This illustrates the cumulative probability up to that point on the curve.
Transcribed Image Text:**(b) Sketch the region corresponding to the statement \( P(z < c) = 0.2 \).** **Shade:** Left of a value. Click and drag the arrows to adjust the values. **Explanation of the Graph:** The image depicts a standard normal distribution curve, which is a bell-shaped curve symmetric around zero. The x-axis is labeled with values ranging from -4 to 4. The area under the curve represents probabilities. In this graph, a region to the left of a value (denoted by \( c \)) is shaded in blue, indicating the probability. The blue shaded area corresponds to \( P(z < c) = 0.2 \), meaning that there is a 20% probability that the random variable \( z \) takes on a value less than \( c \). The shaded region starts at the far left and ends at approximately \( z = -0.84 \), which is marked with an arrow. This illustrates the cumulative probability up to that point on the curve.
### Exploring Probability Regions in Normal Distribution #### Objective: To sketch the region corresponding to the statement \( P(z < c) = 0.2 \). #### Instructions: **Shade:** Users can select how they want to shade the area under the curve. Options include: - Left of a value - Right of a value - Between two values - Two regions In this scenario, the "Left of a value" option is selected to represent the area to the left of a critical point \( c \). #### Graph Explanation: - The graph is a standard normal distribution curve (bell-shaped). - The x-axis ranges from -4 to 4, indicating standard deviations from the mean. - The critical point \( c \) is marked at approximately -1.5 on the x-axis. - The shaded area under the curve to the left of \( c \) represents a probability of 0.2, indicating that 20% of the data falls within this region. #### Interactive Element: Users can click and drag arrows on the graph to adjust the critical value \( c \) and observe how the shaded region changes, helping them understand how probabilities in a normal distribution are affected by different \( z \)-scores.
Transcribed Image Text:### Exploring Probability Regions in Normal Distribution #### Objective: To sketch the region corresponding to the statement \( P(z < c) = 0.2 \). #### Instructions: **Shade:** Users can select how they want to shade the area under the curve. Options include: - Left of a value - Right of a value - Between two values - Two regions In this scenario, the "Left of a value" option is selected to represent the area to the left of a critical point \( c \). #### Graph Explanation: - The graph is a standard normal distribution curve (bell-shaped). - The x-axis ranges from -4 to 4, indicating standard deviations from the mean. - The critical point \( c \) is marked at approximately -1.5 on the x-axis. - The shaded area under the curve to the left of \( c \) represents a probability of 0.2, indicating that 20% of the data falls within this region. #### Interactive Element: Users can click and drag arrows on the graph to adjust the critical value \( c \) and observe how the shaded region changes, helping them understand how probabilities in a normal distribution are affected by different \( z \)-scores.
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