Question

• 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. Find the 70th percentile for the lifetime of one battery.

2. Write an interpretation (a sentence) of the 70th percentile for the lifetime of one battery. Your interpretation should include the value of the 70th percentile with correct units.

3. Draw a graph to represent the 70th percentile. Shade an appropriate region that has area 0.70.

4. Find the probability that the average lifetime of 16 batteries is between 20 and 25 hour. Draw a graph to represent the probability.  Shade an appropriate region.

5. Find the 70th percentile for the average lifetime of 16 batteries. Draw a graph to represent the 70th percentile, Shade an appropriate region that has area 0.70.

Answer 1