The weight of tomatoes chosen at random from a bin at the farmer’s market follows a Normal Distribution with mean u= 10 ounces and standard deviation o = 1 ounce. Suppose we pick two tomatoes at random from the bin and find their total weight T. The random T is : **Title: Understanding Normal Distribution in Random Sampling****Introduction:**The weight of tomatoes chosen at random from a bin at the farmer’s market follows a normal distribution. This particular distribution has a mean \( \mu = 10 \) ounces and a standard deviation \( \sigma = 1 \) ounce. Suppose we pick two tomatoes at random from the bin and find their total weight \( T \). The random variable \( T \) represents this combined weight.**Hint:**Think of the tomatoes as coming from two different distributions.**Options for the Distribution of \( T \):**A. **Normal Distribution** - Mean (\( \mu_T \)): 20 ounces - Standard Deviation (\( \sigma_T \)): 1.41 ounces - *Instruction:* Go to Question #2B. **Normal Distribution** - Mean (\( \mu_T \)): 10 ounces - Standard Deviation (\( \sigma_T \)): 1 ounce - *Instruction:* Go to Question #1C. **Normal Distribution** - Mean (\( \mu_T \)): 20 ounces - Standard Deviation (\( \sigma_T \)): 2 ounces - *Instruction:* Go to Question #3D. **Normal Distribution** - Mean (\( \mu_T \)): 10 ounces - Standard Deviation (\( \sigma_T \)): 2 ounces - *Instruction:* Go to Question #4**Further Explanation:**When dealing with the sum of two independent normal random variables, the means are added, and the variances (the square of the standard deviations) are also added. This exercise helps to explore these concepts and guide students in identifying the right distribution parameters for combined weights.**End Note:**Carefully analyze each description, and use the hints provided to guide your understanding of which distribution fits the random variable \( T \).

Answered: The weight of tomatoes chosen at random…

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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The weight of tomatoes chosen at random from a bin at the farmer’s market follows a Normal Distribution with mean u= 10 ounces and standard deviation o = 1 ounce. Suppose we pick two tomatoes at random from the bin and find their total weight T. The random T is :

**Title: Understanding Normal Distribution in Random Sampling**

**Introduction:**
The weight of tomatoes chosen at random from a bin at the farmer’s market follows a normal distribution. This particular distribution has a mean \( \mu = 10 \) ounces and a standard deviation \( \sigma = 1 \) ounce. Suppose we pick two tomatoes at random from the bin and find their total weight \( T \). The random variable \( T \) represents this combined weight.

**Hint:**
Think of the tomatoes as coming from two different distributions.

**Options for the Distribution of \( T \):**

A. **Normal Distribution**
- Mean (\( \mu_T \)): 20 ounces
- Standard Deviation (\( \sigma_T \)): 1.41 ounces
- *Instruction:* Go to Question #2

B. **Normal Distribution**
- Mean (\( \mu_T \)): 10 ounces
- Standard Deviation (\( \sigma_T \)): 1 ounce
- *Instruction:* Go to Question #1

C. **Normal Distribution**
- Mean (\( \mu_T \)): 20 ounces
- Standard Deviation (\( \sigma_T \)): 2 ounces
- *Instruction:* Go to Question #3

D. **Normal Distribution**
- Mean (\( \mu_T \)): 10 ounces
- Standard Deviation (\( \sigma_T \)): 2 ounces
- *Instruction:* Go to Question #4

**Further Explanation:**
When dealing with the sum of two independent normal random variables, the means are added, and the variances (the square of the standard deviations) are also added. This exercise helps to explore these concepts and guide students in identifying the right distribution parameters for combined weights.

**End Note:**
Carefully analyze each description, and use the hints provided to guide your understanding of which distribution fits the random variable \( T \).

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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