Ignore question #4 please help answer 5&6 since they are connected. Thanks!

tudent Learning Outcome:

• The student will examine properties of the Central Limit Theorem for averages.

Use correct units where appropriate (inches, years, etc). The axes of graphs should be drawn with a ruler or computer. Work will be graded for neatness, completeness and correctness.

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.

The random variable X is the average lifetime of a certain kind of battery.

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

X~ Exp(20)

3. Find the probability that the lifetime of one battery is between 20 and 25 hours.

P (20 X 25) = 0.0814

4. Draw a graph to represent the probability in #3. Shade an appropriate region.

5.what isthe 70th percentile for the lifetime of one battery.

6. an interpretation of the 70th percentile for the lifetime of one battery. Your interpretation should include the value of the 70th percentile with correct units.