Assume the random variable x is normally distributed with mean u= 83 and standard deviation o=4. Find the indic P(x<79) P(x <79) = (Round to four decimal places as needed.)
Assume the random variable x is normally distributed with mean u= 83 and standard deviation o=4. Find the indic P(x<79) P(x <79) = (Round to four decimal places as needed.)
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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![### Understanding Probability in a Normal Distribution
Assume the random variable \( x \) is normally distributed with a mean \( \mu = 83 \) and a standard deviation \( \sigma = 4 \).
#### Problem Statement
Find the indicated probability:
\[ P(x < 79) \]
#### Calculation Prompt
\[ P(x < 79) = \, \] (Round to four decimal places as needed.)
### Explanation:
Given \( \mu = 83 \) and \( \sigma = 4 \), we're asked to find the probability that the variable \( x \) is less than 79. This involves calculating the area under the normal distribution curve to the left of \( x = 79 \).
To solve this, you would typically use a standard normal distribution table or a calculator with statistical functions, transforming the variable using the z-score formula:
\[ z = \frac{x - \mu}{\sigma} = \frac{79 - 83}{4} = -1 \]
Once the z-score is found, consult the z-table to find the probability associated with \( z = -1 \).
### Interactive Options:
- **Clear all**: Resets inputs to try a different calculation.
- **Check answer**: Verifies if the calculated probability is correct.
### Additional Resources:
For more help, explore the linked external resources or seek assistance through the "Get more help" dropdown.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F026bd461-1467-4394-8d30-2d6a7a09468a%2Fd4f91eea-0ed2-4d13-9d57-f31436c79524%2Fklvuowh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Probability in a Normal Distribution
Assume the random variable \( x \) is normally distributed with a mean \( \mu = 83 \) and a standard deviation \( \sigma = 4 \).
#### Problem Statement
Find the indicated probability:
\[ P(x < 79) \]
#### Calculation Prompt
\[ P(x < 79) = \, \] (Round to four decimal places as needed.)
### Explanation:
Given \( \mu = 83 \) and \( \sigma = 4 \), we're asked to find the probability that the variable \( x \) is less than 79. This involves calculating the area under the normal distribution curve to the left of \( x = 79 \).
To solve this, you would typically use a standard normal distribution table or a calculator with statistical functions, transforming the variable using the z-score formula:
\[ z = \frac{x - \mu}{\sigma} = \frac{79 - 83}{4} = -1 \]
Once the z-score is found, consult the z-table to find the probability associated with \( z = -1 \).
### Interactive Options:
- **Clear all**: Resets inputs to try a different calculation.
- **Check answer**: Verifies if the calculated probability is correct.
### Additional Resources:
For more help, explore the linked external resources or seek assistance through the "Get more help" dropdown.
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