Assume that the readings at freezing or a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between 0.341 °C and 2.715°C. P(0.341 < Z < 2.715) Submit Question =
Assume that the readings at freezing or a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between 0.341 °C and 2.715°C. P(0.341 < Z < 2.715) Submit Question =
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 Normal Distribution in Thermometer Readings
**Problem Statement (Question 10):**
Assume that the readings at freezing or a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between 0.341°C and 2.715°C.
\[ P(0.341 < Z < 2.715) = \]
**Answer and Explanation:**
In this problem, we are working with the standard normal distribution. The standard normal distribution is a normal distribution with a mean (\(\mu\)) of 0 and a standard deviation (\(\sigma\)) of 1. The variable \(Z\) represents the standard normal random variable.
To find the probability that \(0.341 < Z < 2.715\):
1. **Locate the Z-scores:** \(0.341\) and \(2.715\) on the standard normal distribution table, which provides the cumulative probabilities up to a given Z-score.
2. **Find Cumulative Probabilities:**
- The cumulative probability up to \(Z = 0.341\)
- The cumulative probability up to \(Z = 2.715\)
3. **Compute the Desired Probability:**
- Let \(P(Z < 0.341) = A\)
- Let \(P(Z < 2.715) = B\)
- Then, the probability of the thermometer reading between \(0.341°C\) and \(2.715°C\) is \(B - A\).
4. **Interpreting the Result:**
- The value obtained will represent the probability that a randomly chosen thermometer reads between 0.341°C and 2.715°C.
**Note:** To solve this problem, you would typically refer to standard normal distribution (Z) tables or use computational tools such as statistical software or graphing calculators.
**Submit Your Answer:**
After calculating the required probability, submit your result in the designated input box on the platform and click on the "Submit Question" button to proceed.
[Submit Question Button]
\[ \text{Previous Button} \]
---
This page contains a form-like setup with a problem statement and a designated area for inputting answers. Once an answer is determined, it can be submitted for evaluation by clicking on the "Submit Question" button](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3f191a8-a1b2-42ed-ac9e-32d60645d728%2Fec71d3ae-1267-46a8-998a-e6e31f6e4cc8%2F8b2cj89_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Normal Distribution in Thermometer Readings
**Problem Statement (Question 10):**
Assume that the readings at freezing or a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between 0.341°C and 2.715°C.
\[ P(0.341 < Z < 2.715) = \]
**Answer and Explanation:**
In this problem, we are working with the standard normal distribution. The standard normal distribution is a normal distribution with a mean (\(\mu\)) of 0 and a standard deviation (\(\sigma\)) of 1. The variable \(Z\) represents the standard normal random variable.
To find the probability that \(0.341 < Z < 2.715\):
1. **Locate the Z-scores:** \(0.341\) and \(2.715\) on the standard normal distribution table, which provides the cumulative probabilities up to a given Z-score.
2. **Find Cumulative Probabilities:**
- The cumulative probability up to \(Z = 0.341\)
- The cumulative probability up to \(Z = 2.715\)
3. **Compute the Desired Probability:**
- Let \(P(Z < 0.341) = A\)
- Let \(P(Z < 2.715) = B\)
- Then, the probability of the thermometer reading between \(0.341°C\) and \(2.715°C\) is \(B - A\).
4. **Interpreting the Result:**
- The value obtained will represent the probability that a randomly chosen thermometer reads between 0.341°C and 2.715°C.
**Note:** To solve this problem, you would typically refer to standard normal distribution (Z) tables or use computational tools such as statistical software or graphing calculators.
**Submit Your Answer:**
After calculating the required probability, submit your result in the designated input box on the platform and click on the "Submit Question" button to proceed.
[Submit Question Button]
\[ \text{Previous Button} \]
---
This page contains a form-like setup with a problem statement and a designated area for inputting answers. Once an answer is determined, it can be submitted for evaluation by clicking on the "Submit Question" button
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