Assume the random variable x is normally distributed with mean u = 83 and standard deviation a =5. Find the indicated probability. P(69
Assume the random variable x is normally distributed with mean u = 83 and standard deviation a =5. Find the indicated probability. P(69
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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![Certainly! Here’s a transcription of the text that would appear on an educational website:
---
**Problem Statement:**
Assume the random variable \( x \) is normally distributed with mean \( \mu = 83 \) and standard deviation \( \sigma = 5 \). Find the indicated probability.
\[ P(69 < x < 80) \]
---
**Solution Approach:**
To find the probability \( P(69 < x < 80) \) for a normally distributed variable, we use the properties of the normal distribution:
1. **Standardizing the Values:** Convert the range values to standard scores (z-scores) using the formula:
\[
z = \frac{x - \mu}{\sigma}
\]
2. **Calculate the Z-Scores** for the given range:
- For \( x = 69 \):
\[
z = \frac{69 - 83}{5} = -2.8
\]
- For \( x = 80 \):
\[
z = \frac{80 - 83}{5} = -0.6
\]
3. **Use Z-Score Table or Standard Normal Distribution Table** to find the probability corresponding to each z-score, and calculate:
\[
P(-2.8 < z < -0.6)
\]
4. **Result:** The value can be computed using statistical software, calculators with normal distribution functions, or z-tables.
**Round your answer to four decimal places as needed.**
Provide your calculated result below:
\[ P(69 < x < 80) = \_\_\_\_ \]
**Check Your Answer:**
Click "Check answer" once you've computed the probability.
---
Feel free to reach out for further assistance or refer to statistical resources for help in solving normal distribution problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F69170c6b-6ffc-415a-b49a-b0bc6464b186%2F5083a92b-a3cd-43c6-9b81-0e06d4348225%2F8b5v1v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Here’s a transcription of the text that would appear on an educational website:
---
**Problem Statement:**
Assume the random variable \( x \) is normally distributed with mean \( \mu = 83 \) and standard deviation \( \sigma = 5 \). Find the indicated probability.
\[ P(69 < x < 80) \]
---
**Solution Approach:**
To find the probability \( P(69 < x < 80) \) for a normally distributed variable, we use the properties of the normal distribution:
1. **Standardizing the Values:** Convert the range values to standard scores (z-scores) using the formula:
\[
z = \frac{x - \mu}{\sigma}
\]
2. **Calculate the Z-Scores** for the given range:
- For \( x = 69 \):
\[
z = \frac{69 - 83}{5} = -2.8
\]
- For \( x = 80 \):
\[
z = \frac{80 - 83}{5} = -0.6
\]
3. **Use Z-Score Table or Standard Normal Distribution Table** to find the probability corresponding to each z-score, and calculate:
\[
P(-2.8 < z < -0.6)
\]
4. **Result:** The value can be computed using statistical software, calculators with normal distribution functions, or z-tables.
**Round your answer to four decimal places as needed.**
Provide your calculated result below:
\[ P(69 < x < 80) = \_\_\_\_ \]
**Check Your Answer:**
Click "Check answer" once you've computed the probability.
---
Feel free to reach out for further assistance or refer to statistical resources for help in solving normal distribution problems.
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