The lifetime of a certain kind of battery is exponentially distributed, with an average lifetime of 20 hours.

1. We are interested in the lifetime of one battery. Define the random variable X in words.

2. Give the distribution of X using numbers, letters and symbols as appropriate.

X~_______________

3. Find the probability that the lifetime of one battery is between 18 and 21 hours.

4. Find the value of the 75^th percentile for the lifetime of one battery. Remember units!

5. Write an interpretation (a sentence) of the 75^th percentile for the lifetime of one battery. Your interpretation should include the value of the 75^th percentile with correct units.

6. We are interested in the average lifetime of 25 of these batteries. Call this random variable . In words, define .

7. Give the distribution of . ~__________

8. Find the probability that the average lifetime of 25 batteries is between 18 and 21 hours.

9. Find the value of the 75^th percentile for the average lifetime of 25 batteries. Remember units!

FOUR GRAPHS (remember you are uploading ONE file for this project, so be sure to include your graphs in the one file you upload):

10. Draw a graph to represent the probability that the lifetime of one battery is between 18 and 21 hours. Shade an appropriate region. (See Question 3)

11. Draw a graph to represent the 75^th percentile for the lifetime of one battery. Shade an appropriate region that has area 0.75. (See Question 4)

12. Draw a graph to represent the probability that the average lifetime of 25 batteries is between 18 and 21 hours. Shade an appropriate region. (See Question 8)

13. Draw a graph to represent the 75^th percentile for the average lifetime of 25 batteries. Shade an appropriate region that has area 0.75. (See Question 9)