MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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**Standard Normal Distribution**

**Problem Statement:**
Let \( z \) be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)

**Task:**
\[ P(z < -0.8) = \]

Shade the corresponding area under the standard normal curve.

**Diagrams:**

There are four graphs depicting the standard normal distribution, each with a curve representing the probability density function of the standard normal variable \( z \).

1. **Graph 1:**
   - The curve is symmetrical about the y-axis.
   - The shaded region is on the left side of the curve from approximately \( z = -3 \) to \( z = -0.8 \).

2. **Graph 2:**
   - The curve remains symmetrical about the y-axis.
   - The shaded region is on the right side of the curve from approximately \( z = 0.8 \) to \( z = 3 \).

3. **Graph 3:**
   - The curve is similarly symmetrical about the y-axis.
   - The entire area under the curve is shaded, covering all values from \( z = -3 \) to \( z = 3 \).

4. **Graph 4:**
   - The curve retains its symmetrical property.
   - The correctly shaded region corresponds to the left tail of the curve, extending from \( z = -3 \) to \( z = -0.8 \).

A green check mark indicates that Graph 4 correctly represents the shaded area for \( P(z < -0.8) \) under the standard normal curve.
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Transcribed Image Text:**Standard Normal Distribution** **Problem Statement:** Let \( z \) be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.) **Task:** \[ P(z < -0.8) = \] Shade the corresponding area under the standard normal curve. **Diagrams:** There are four graphs depicting the standard normal distribution, each with a curve representing the probability density function of the standard normal variable \( z \). 1. **Graph 1:** - The curve is symmetrical about the y-axis. - The shaded region is on the left side of the curve from approximately \( z = -3 \) to \( z = -0.8 \). 2. **Graph 2:** - The curve remains symmetrical about the y-axis. - The shaded region is on the right side of the curve from approximately \( z = 0.8 \) to \( z = 3 \). 3. **Graph 3:** - The curve is similarly symmetrical about the y-axis. - The entire area under the curve is shaded, covering all values from \( z = -3 \) to \( z = 3 \). 4. **Graph 4:** - The curve retains its symmetrical property. - The correctly shaded region corresponds to the left tail of the curve, extending from \( z = -3 \) to \( z = -0.8 \). A green check mark indicates that Graph 4 correctly represents the shaded area for \( P(z < -0.8) \) under the standard normal curve.
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