The processing time for the robogate has a normal distribution with mean 21 sec and standard deviation 3 sec. Find the probability that the next operation of the robogate will take 27.9 sec or less. Click the icon to view the standard normal distribution table. *** The probability is
The processing time for the robogate has a normal distribution with mean 21 sec and standard deviation 3 sec. Find the probability that the next operation of the robogate will take 27.9 sec or less. Click the icon to view the standard normal distribution table. *** The probability is
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Question
![### Problem Statement
The processing time for the robogate has a normal distribution with a mean of 21 seconds and a standard deviation of 3 seconds. Find the probability that the next operation of the robogate will take 27.9 seconds or less.
### Instructions
Click the icon to view the standard normal distribution table.
---
### Solution
The probability is [blank space for user input].
---
### Explanation
In this problem, we need to calculate the probability that the robogate's processing time will be 27.9 seconds or less. Given the normal distribution parameters (mean and standard deviation), we can standardize this value and use the Z-table (standard normal distribution table) to find the corresponding probability.
### Steps to Solve
1. **Calculate the Z-score:**
\[
Z = \frac{X - \mu}{\sigma}
\]
where \(X\) is 27.9 seconds, \(\mu\) is 21 seconds, and \(\sigma\) is 3 seconds.
2. **Find the Z-score in the standard normal distribution table** to determine the probability that corresponds to the calculated Z value.
### Standard Normal Distribution Table
The standard normal distribution table (also known as the Z-table) helps in finding the cumulative probability up to a given Z-score for a standard normal distribution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8bde779e-c68e-4dd4-a0b8-70b65f5ae251%2F688565c6-d352-425d-9816-0f53b493aa7b%2Frtc5fxf_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
The processing time for the robogate has a normal distribution with a mean of 21 seconds and a standard deviation of 3 seconds. Find the probability that the next operation of the robogate will take 27.9 seconds or less.
### Instructions
Click the icon to view the standard normal distribution table.
---
### Solution
The probability is [blank space for user input].
---
### Explanation
In this problem, we need to calculate the probability that the robogate's processing time will be 27.9 seconds or less. Given the normal distribution parameters (mean and standard deviation), we can standardize this value and use the Z-table (standard normal distribution table) to find the corresponding probability.
### Steps to Solve
1. **Calculate the Z-score:**
\[
Z = \frac{X - \mu}{\sigma}
\]
where \(X\) is 27.9 seconds, \(\mu\) is 21 seconds, and \(\sigma\) is 3 seconds.
2. **Find the Z-score in the standard normal distribution table** to determine the probability that corresponds to the calculated Z value.
### Standard Normal Distribution Table
The standard normal distribution table (also known as the Z-table) helps in finding the cumulative probability up to a given Z-score for a standard normal distribution.
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