1. No Tutoring Today! Warm-Up… Quickwrite…
Find the indicated probabilities
Quickwrite…
When was the last time you bought something and returned it due to a problem?
Ex: “The last time I returned something was when _____ ______________________.”

2. Compare and Explain… your Warm-Up starting with Student #3 (1 min)
0.0016
0.0918

3. Round Robin…
starting with the student sitting closest to the door (1 min)
When was the last time you bought something and returned it due to a problem?
Ex: “The last time I returned something was when _______________.”

4. Homework Answers
Find the indicated
probabilities
0.2286
0.0471

5. Inverse normal distribution

6. Inverse Normal Probability Distribution
Sometimes we need to find z or x values that correspond to a given area under the normal curve
This situation arises when we want to specify a guarantee period similar to yesterday’s practice problem
In such cases, we use the standard normal distribution table “in reverse”
When we look up an area and find the corresponding z value, we are using the inverse normal probability distribution

7. Example
Apple plans to sell an expensive new computer, so the company wants to advertise an impressive guarantee for the life expectancy of its computer control system
The guarantee policy will refund the full purchase price if the computer fails during the guarantee period
The research department has done tests that show that the mean life for the computer is 30 months, with standard deviation of 4 months

8. Example
How long can the guarantee period be if management does not want to refund the purchase price on more than 7% of the Apple computers?
We can see the distribution of lifetimes for the computer control system in which the computer lasts fewer months than the guarantee period
7% of the Computers Have a Lifetime Less Than the Guarantee Period

9. Example
If a computer system lasts fewer months than the guarantee period, a full-price refund will have to be made
We can use a table to find the z value such that 7% of the total area under the standard normal curve lies to the left of the z value
The area value is , which is not in our table, so we use the closest area,
The corresponding z value of z = –1.48

10. Example
To translate this value back to an x value (in months), we use the formula x = z + 
= –1.48(4) (Use  = 4 months and  = 30 months.)
= months
What does this mean for Apple?
The company can guarantee the new computers for x = 24 months
For this guarantee period, they expect to refund the purchase price of no more than 7% of the computers

11. Practice

13. Go on Socrative and answer today’s…
Reflection Question: What question(s) do you still have from today's lesson?