9. What is the probability that a randomly selected elephant will weight at least 8.56 tons? 856 10. What is the probability that a randomly selected elephant will have a weight that is at most 6.42 tons? 642 11. What is the probability that a randomly selected elephant will weigh between 3.21 and 9.63 tons? 321

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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I need help with 9-11 please

**The Empirical Rule**

The average weight of an elephant is 6.42 tons with a standard deviation of 1.07 tons. Use the Empirical Rule to answer the following questions.

1. **What weight is 3 standard deviations below the mean?**  
   - Answer: 3.21

2. **What weight is 2 standard deviations below the mean?**  
   - Answer: 4.28

3. **What weight is 1 standard deviation below the mean?**  
   - Answer: 5.35

4. **What weight is the mean?**  
   - Answer: 6.42

5. **What weight is 1 standard deviation above the mean?**  
   - Answer: 7.49

6. **What weight is 2 standard deviations above the mean?**  
   - Answer: 8.56

7. **What weight is 3 standard deviations above the mean?**  
   - Answer: 9.63

8. **Between what two values do 68% of elephants weigh?**  
   - Answer: Between 5.35 and 7.49

9. **What is the probability that a randomly selected elephant will weigh at least 8.56 tons?**  
   - Answer: Incorrect calculation (the correct probability should be around 16%).

10. **What is the probability that a randomly selected elephant will have a weight that is at most 6.42 tons?**  
    - Answer: Incorrect calculation (the correct probability should be 50%).

11. **What is the probability that a randomly selected elephant will weigh between 3.21 and 9.63 tons?**  
    - Answer: Incorrect calculation (the correct probability should be 99.7%).

12. **Would a weight of 3 tons be an unusual weight for an elephant?**  
    - Answer: Yes, 3 tons is beyond 3 standard deviations of the mean.
Transcribed Image Text:**The Empirical Rule** The average weight of an elephant is 6.42 tons with a standard deviation of 1.07 tons. Use the Empirical Rule to answer the following questions. 1. **What weight is 3 standard deviations below the mean?** - Answer: 3.21 2. **What weight is 2 standard deviations below the mean?** - Answer: 4.28 3. **What weight is 1 standard deviation below the mean?** - Answer: 5.35 4. **What weight is the mean?** - Answer: 6.42 5. **What weight is 1 standard deviation above the mean?** - Answer: 7.49 6. **What weight is 2 standard deviations above the mean?** - Answer: 8.56 7. **What weight is 3 standard deviations above the mean?** - Answer: 9.63 8. **Between what two values do 68% of elephants weigh?** - Answer: Between 5.35 and 7.49 9. **What is the probability that a randomly selected elephant will weigh at least 8.56 tons?** - Answer: Incorrect calculation (the correct probability should be around 16%). 10. **What is the probability that a randomly selected elephant will have a weight that is at most 6.42 tons?** - Answer: Incorrect calculation (the correct probability should be 50%). 11. **What is the probability that a randomly selected elephant will weigh between 3.21 and 9.63 tons?** - Answer: Incorrect calculation (the correct probability should be 99.7%). 12. **Would a weight of 3 tons be an unusual weight for an elephant?** - Answer: Yes, 3 tons is beyond 3 standard deviations of the mean.
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