Let z be a random variable vith a standard normal distribution. Find the indicated probability. (Round your ansvwer to four decimal places. P(zs -0.8) = [ Shade the corresponding area under the standard normal curve. 0,4 0,4 0.3 0.3 02 0.2 0.1 0.1 -1 o-3 -2 2.
Let z be a random variable vith a standard normal distribution. Find the indicated probability. (Round your ansvwer to four decimal places. P(zs -0.8) = [ Shade the corresponding area under the standard normal curve. 0,4 0,4 0.3 0.3 02 0.2 0.1 0.1 -1 o-3 -2 2.
MATLAB: An Introduction with Applications
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F890db880-490b-4ebd-8134-9ade3709eb7e%2Fdfc64e95-d71f-4f22-a8dd-8064a41673a0%2F7sfc47t_processed.png&w=3840&q=75)
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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