Question

The lifetime of a certain kind of battery is exponentially distributed, with an average lifetime of 25 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.

6. We are interested in the average lifetime of 16 of these batteries. Call this random variable. In words, define.

7. Give the distribution of. ~__________

8. Find the probability that the average lifetime of 16 batteries is between 20 and 25 hours.

9. Find the value of the 60th percentile for the average lifetime of 16 batteries. Remember units!

Answer 1

Let X is a random variable shows the lifetime of battery. Here X has exponential distribution with parameter

4:

The percentile formula of exponential distribution is

Here we need 60th percentile so

5:

It shows that 60% of time lifetime of battery is less than equal to 22.91 hours.

6:

The distribution of average lifetime of 16 batteries will be sampling distribution of sample mean. This distribution will be approximately normally distributed.

Since X has exponetial distribution so mean and SD of X will be

7:

The sampling distribution of sample mean will be as follow:

8:

9:

------------------------------------------------------------------------------