ng time for the robogate has a normal distri will take 27 sec or less. icon to view the standard normal distributi
ng time for the robogate has a normal distri will take 27 sec or less. icon to view the standard normal distributi
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![### Normal Distribution Problem
The processing time for the robogate has a normal distribution with a mean (\(\mu\)) of 21 seconds and a standard deviation (\(\sigma\)) of 3 seconds. Find the probability that the next operation of the robogate will take 27 seconds or less.
---
**Visual Aid**: There is an icon representing a standard normal distribution table, which can be clicked to assist in solving the problem.
---
**Solution**:
Step-by-step we solve for the probability:
1. **Compute the Z-Score**:
\[
Z = \frac{X - \mu}{\sigma}
\]
Where \( X = 27 \) seconds, \( \mu = 21 \) seconds, and \( \sigma = 3 \) seconds.
\[
Z = \frac{27 - 21}{3} = \frac{6}{3} = 2
\]
2. **Find the probability associated with the Z-Score**:
Using the standard normal distribution table (click the icon to view it), locate the probability for \( Z = 2 \).
The Z-Score of 2 corresponds to a cumulative probability of approximately 0.9772.
---
### Result
The probability that the next operation of the robogate will take 27 seconds or less is 0.9772.
\[
\boxed{0.9772}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc56b3bff-26b7-4f28-9b8d-5c65e8bb1b58%2Fda0cea2b-8b6f-4863-bfd4-c7e3d14b5338%2Fx8f67m9_processed.png&w=3840&q=75)
Transcribed Image Text:### Normal Distribution Problem
The processing time for the robogate has a normal distribution with a mean (\(\mu\)) of 21 seconds and a standard deviation (\(\sigma\)) of 3 seconds. Find the probability that the next operation of the robogate will take 27 seconds or less.
---
**Visual Aid**: There is an icon representing a standard normal distribution table, which can be clicked to assist in solving the problem.
---
**Solution**:
Step-by-step we solve for the probability:
1. **Compute the Z-Score**:
\[
Z = \frac{X - \mu}{\sigma}
\]
Where \( X = 27 \) seconds, \( \mu = 21 \) seconds, and \( \sigma = 3 \) seconds.
\[
Z = \frac{27 - 21}{3} = \frac{6}{3} = 2
\]
2. **Find the probability associated with the Z-Score**:
Using the standard normal distribution table (click the icon to view it), locate the probability for \( Z = 2 \).
The Z-Score of 2 corresponds to a cumulative probability of approximately 0.9772.
---
### Result
The probability that the next operation of the robogate will take 27 seconds or less is 0.9772.
\[
\boxed{0.9772}
\]
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