7. A manufacturer of high intensity lamps finds that the useful life of the lamps is normally distributed with population mean = 70 months and population standard deviation s = 12 months. The manufacturer wants to write a warranty so that only 1.5% (0.015) of the lamps fail while still under warranty. For how long should the warranty be written?

8. The time required for laboratory rats to complete a maze is normally distributed with population mean = 45 minutes with population standard deviation = 5.4 minutes. What proportion of the rats complete the maze with time between 37 to 53 minutes?

9. The useful life of a type of a type of washing machines is normally distributed. (Useful life means me the time before the machines needs to be repaired.) The population mean = 84 months and population standard deviation = 8 months. The manufacturer wants to write the warranty so only 2% (0.02) of the machines will need to be repaired while still under warranty. For how long should the warranty be written?