10. A wireless phone company manufactures cell phone chips for 40% of the cell phones it produces and purchases chips for the remaining 60% of its cell phone production from a supplier. Suppose that the lifetime of a chip manufactured by the company’s own plant is gamma with mean 4 and variance 4 years whereas the lifetime of a chip purchased from the supplier is gamma with mean 6 and standard deviation 6 years. The company offers its customers a one year replacement warranty. Find the percentage of the cell phones that must be replaced by the company due to chip failure.

Hint: LetX be the lifetime of the chip of a randomly selected cell phonemanufactured by the wireless phone company. Let A be the event that the chip was manufactured by the company’s own plant. Use the law of total probability to find P(X ≤ 1).