Use computer language R to answer the following question

A cell phone manufacturer is considering to offer a refund to its customers whose battery fails before 5 years. The refunds start at $10, and increase by $1.50 for every month the battery falls short of 5 years. For example, a customer whose battery fails after 4 years and 6 months would receive a refund of $19. A customer whose battery fails after 5 years would receive no refund. Previous studies show that a batterys life is normally distributed with a mean of 7 years and standard deviation of 2 years. Develop a simulation with 100,000 trials for the amount of a refund.

According to your simulation, what is the expected cost per cell phone to the manufacturer of this offer?

According to your simulation, what is the probability a refund will be paid?

According to your simulation, what is the average cost per refund?