The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3484 grams and a variance of 160,000. If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be greater than 4124 grams. Round your answer to four decimal places.
The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3484 grams and a variance of 160,000. If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be greater than 4124 grams. Round your answer to four decimal places.
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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![**Educational Content: Normal Distribution and Probability**
The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3484 grams and a variance of 160,000. If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be greater than 4124 grams. Round your answer to four decimal places.
**Answer Explanation:**
To solve this problem, you can use a normal distribution table (also known as a z-table) to find the probability. You need to find the z-score for 4124 grams and then use the table to determine the probability that a baby's weight is greater than this value.
**Instructions:**
1. **Calculate the Z-Score:**
\[
z = \frac{X - \mu}{\sigma}
\]
where \( X \) is 4124 grams, \( \mu \) is the mean (3484 grams), and \( \sigma \) is the standard deviation. The standard deviation is the square root of the variance.
2. **Use the Normal Table:**
- You can select a normal table (z to \( \infty \)) by clicking the appropriate option below.
- Enter the calculated z-score to find the corresponding probability.
**Tools and Navigation:**
- The interface provides tables and a keypad for input.
- Use keyboard shortcuts for quick access.
- To view a value in a table, select the desired table, click the cell at the row and column intersection, or navigate using arrow keys. Select the appropriate cell by pressing the Space key.
**Interactive Elements:**
- Two buttons labeled "Normal Table - ∞ to z" help in determining probabilities from z-scores.
- A text box is available for entering calculated values.
**Interface Features:**
- Submit your answer using the "Submit Answer" button after calculations.
- Access date and time from the toolbar (e.g., Oct 27, 6:25 PM).
**Image Description:**
This image shows a laptop screen displaying instructions for calculating probabilities using normal distribution tables. The interface consists of options for tables, input boxes, and submission tools.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa82f53e3-5ace-487b-ad28-8a22d3abf18a%2Ffe377092-92c0-46aa-89b0-9afac9f3c504%2Fyb1jndb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Content: Normal Distribution and Probability**
The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3484 grams and a variance of 160,000. If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be greater than 4124 grams. Round your answer to four decimal places.
**Answer Explanation:**
To solve this problem, you can use a normal distribution table (also known as a z-table) to find the probability. You need to find the z-score for 4124 grams and then use the table to determine the probability that a baby's weight is greater than this value.
**Instructions:**
1. **Calculate the Z-Score:**
\[
z = \frac{X - \mu}{\sigma}
\]
where \( X \) is 4124 grams, \( \mu \) is the mean (3484 grams), and \( \sigma \) is the standard deviation. The standard deviation is the square root of the variance.
2. **Use the Normal Table:**
- You can select a normal table (z to \( \infty \)) by clicking the appropriate option below.
- Enter the calculated z-score to find the corresponding probability.
**Tools and Navigation:**
- The interface provides tables and a keypad for input.
- Use keyboard shortcuts for quick access.
- To view a value in a table, select the desired table, click the cell at the row and column intersection, or navigate using arrow keys. Select the appropriate cell by pressing the Space key.
**Interactive Elements:**
- Two buttons labeled "Normal Table - ∞ to z" help in determining probabilities from z-scores.
- A text box is available for entering calculated values.
**Interface Features:**
- Submit your answer using the "Submit Answer" button after calculations.
- Access date and time from the toolbar (e.g., Oct 27, 6:25 PM).
**Image Description:**
This image shows a laptop screen displaying instructions for calculating probabilities using normal distribution tables. The interface consists of options for tables, input boxes, and submission tools.
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