Mr. Voss and Mr. Cull bowl every Tuesday night. Over the been approximately Normally distributed with a mean of 2 During the same period, Mr. Cull's scores have also been : a mean of 230 and a standard deviation of 40. a. Assuming their scores are independent, what is the than Mr. Cull on a randomly-selected Tuesday nigl V: M=212 6= 3| C: M=230 6=40 M=212- b. Assuming their scores are independent, what is 50 points higher than Mr. Voss on a randomly-:

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**Text Transcription for Educational Website:**

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**3. Problem Analysis**

**Scenario:** Mr. Voss and Mr. Cull bowl every Tuesday night. Over the past few years, Mr. Voss's scores have been approximately normally distributed with a mean of 212 and a standard deviation of 31. During the same period, Mr. Cull’s scores have also been approximately normally distributed with a mean of 230 and a standard deviation of 40.

a. **Analysis Question:** Assuming their scores are independent, what is the probability that Mr. Voss scores higher than Mr. Cull on a randomly-selected Tuesday night?

- **Calculation Details:**  
  \( V: \, \text{Mean} = 212, \, \text{Standard Deviation} = 31 \)  
  \( C: \, \text{Mean} = 230, \, \text{Standard Deviation} = 40 \)
  
  Calculation:  
  \( V = 212 - 230 = -18 \)

b. **Analysis Question:** Assuming their scores are independent, what is the probability that Mr. Cull scores more than 50 points higher than Mr. Voss on a randomly-selected Tuesday night?

---

**Handwritten Notes Interpretation:**

- There are brief handwritten calculations outlining the difference in mean scores between Mr. Voss and Mr. Cull, indicating step-by-step analysis for determining probabilities. Further detailed steps would be necessary to calculate probabilities using Z-scores or other statistical methods.
Transcribed Image Text:**Text Transcription for Educational Website:** --- **3. Problem Analysis** **Scenario:** Mr. Voss and Mr. Cull bowl every Tuesday night. Over the past few years, Mr. Voss's scores have been approximately normally distributed with a mean of 212 and a standard deviation of 31. During the same period, Mr. Cull’s scores have also been approximately normally distributed with a mean of 230 and a standard deviation of 40. a. **Analysis Question:** Assuming their scores are independent, what is the probability that Mr. Voss scores higher than Mr. Cull on a randomly-selected Tuesday night? - **Calculation Details:** \( V: \, \text{Mean} = 212, \, \text{Standard Deviation} = 31 \) \( C: \, \text{Mean} = 230, \, \text{Standard Deviation} = 40 \) Calculation: \( V = 212 - 230 = -18 \) b. **Analysis Question:** Assuming their scores are independent, what is the probability that Mr. Cull scores more than 50 points higher than Mr. Voss on a randomly-selected Tuesday night? --- **Handwritten Notes Interpretation:** - There are brief handwritten calculations outlining the difference in mean scores between Mr. Voss and Mr. Cull, indicating step-by-step analysis for determining probabilities. Further detailed steps would be necessary to calculate probabilities using Z-scores or other statistical methods.
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