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 :

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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 \( T \).
Transcribed Image Text:**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 \( T \).
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