o) L 27%E]! Documents ED 33 Chapter7Project @ 4 Search 1219 PM Mon Nov1 Chapter 7: Central Limit Theorem (CLT) Names: Student Learning Outcome: The student will examine properties of the Central Limit Theorem for averages. I The student will draw 4 graphs illustrating the exponential and normal distributions. NOTES: Use correct units where appropriate (inches, years, etc) for percentiles. The horizontal axis of each graph should be drawn with a ruler or computer The horizontal axis of each graph should be labelled either X or X The horizontal axis of each graph should be scaled (this means at least 2 numbers on the axis). Work will be graded for neatness, completeness and correctness. Distributions we know are B(n,p), U(a,b), Exp(m), N(mean, standard deviation) 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. Dene 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 22 hours. 4. Find the value of the 60th percentile for the lifetime of one battery. Remember units! 5. Write an interpretation (a sentence) of the 60th percentile for the lifetime of one battery. Your interpretation should include the value of the 60th percentile with correct units. 4 Search 1219 PM Mon Nov1 '6' t 27%E} Documents ED 33 Chapter7Project @ 6. We are interested in the average lifetime of 25 of these batteries. Call this random variable X. In words, dene X . 7. Give the distribution of f. 14 8. Find the probability that the average lifetime of 25 batteries is between 18 and 22 hours. 9. Find the value of the 60th percentile for the average lifetime of 25 batteries. Remember units! FOUR GRAPHS (remember you are uploading ONE le for this project, so be sure to include your graphs in the one le you upload): 10. Draw a graph to represent the probability that the lifetime of one battery is between 18 and 22 hours. Shade an appropriate region. (See Question 3) 11. Draw a graph to represent the 60th percentile for the lifetime of one battery. Shade an appropriate region that has area 0.60. (See Question 4) 12. Draw a graph to represent the probability that the average lifetime of 25 batteries is between 18 and 22 hours. Shade an appropriate region. (See Question 8) 13. Draw a graph to represent the 60th percentile for the average lifetime of 25 batteries. Shade an appropriate region that has area 0.60. (See Question 9)