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 _____ ______________________.”

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

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 _______________.”

Homework Answers Find the indicated probabilities 0.2286 0.0471

Inverse normal distribution

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

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

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

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 0.0700, which is not in our table, so we use the closest area, 0.0694 The corresponding z value of z = –1.48

Example To translate this value back to an x value (in months), we use the formula x = z +  = –1.48(4) + 30 (Use  = 4 months and  = 30 months.) = 24.08 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

Practice

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