Apple just introduced EarPods Pro V in three colors: conventional white, glorious gold, and fiery red. Apple think that quarterly demand for white pods will follow a normal random variable with mean 12 (millions) and standard deviation 2.5 (millions), quarterly demand for gold pods will follow a normal random variable with mean 7.0 (millions) and standard deviation 2.5 (millions), and quarterly demand for red pods will follow a normal random variable with mean 4.0 (millions) and standard deviation 1.5 (millions). Assume that demand for each color is independent on each other.

Use this information for the next 4 questions.

13. Currently, Apple plans to stock up 13 million white pods for the quarter. What is the probability that Apple will experience a stock out of white pods?

14. If Apple wants to provide a 97% service level for the white pods, what is the desired inventory level for the white pods?

15. Several investment banks predict that the total quarterly demand of the new EarPods Pro V will be no more than 25 million units. What is the probability that their prediction is correct?

16. Apple will consider the colored EarPods as a success and will introduce more colors in the next line up if the demand for the two colored EarPods (Red and Gold) exceeds the demand of white EarPods. What is the probability that the demand for colored EarPods exceeds the demand for the white EarPods?