b. 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? Pix<-50) Q 2636
b. 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? Pix<-50) Q 2636
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
3b
![**Problem 3: Analyzing Bowling Scores Using Probability**
Over the past few years, Mr. Voss and Mr. Cull bowl every Tuesday night. Their scores have been approximately Normally distributed as follows:
- **Mr. Voss's Scores:**
- Mean (\( \mu \)): 212
- Standard deviation (\( \sigma \)): 31
- **Mr. Cull's Scores:**
- Mean (\( \mu \)): 230
- Standard deviation (\( \sigma \)): 40
**a. Probability that Mr. Voss Scores Higher than Mr. Cull**
Assuming their scores are independent, calculate the probability that Mr. Voss scores higher than Mr. Cull on a randomly-selected Tuesday night.
**b. Probability that Mr. Cull Scores More than 50 Points Higher than Mr. Voss**
Assuming their scores are independent, calculate the probability that Mr. Cull scores more than 50 points higher than Mr. Voss on a randomly-selected Tuesday night.
**Written Calculations:**
- The calculation for the standard deviation of the difference in scores:
\[
\sqrt{31^2 + 40^2} = 50.6
\]
- To find \( P(X < 50) \), it seems to be approximated as 0.326.
This information guides the calculations for determining probabilities based on normal distribution properties.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02c99683-a01b-4e64-96f8-7137fedec6c4%2F6c1237f2-84ec-4275-b7f4-579f01294322%2F9r0hsk2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 3: Analyzing Bowling Scores Using Probability**
Over the past few years, Mr. Voss and Mr. Cull bowl every Tuesday night. Their scores have been approximately Normally distributed as follows:
- **Mr. Voss's Scores:**
- Mean (\( \mu \)): 212
- Standard deviation (\( \sigma \)): 31
- **Mr. Cull's Scores:**
- Mean (\( \mu \)): 230
- Standard deviation (\( \sigma \)): 40
**a. Probability that Mr. Voss Scores Higher than Mr. Cull**
Assuming their scores are independent, calculate the probability that Mr. Voss scores higher than Mr. Cull on a randomly-selected Tuesday night.
**b. Probability that Mr. Cull Scores More than 50 Points Higher than Mr. Voss**
Assuming their scores are independent, calculate the probability that Mr. Cull scores more than 50 points higher than Mr. Voss on a randomly-selected Tuesday night.
**Written Calculations:**
- The calculation for the standard deviation of the difference in scores:
\[
\sqrt{31^2 + 40^2} = 50.6
\]
- To find \( P(X < 50) \), it seems to be approximated as 0.326.
This information guides the calculations for determining probabilities based on normal distribution properties.
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