Manufacturer of a well known audio speaker business has determined that it's new line of speakers have a service life that can be modeled by a normal distribution with a mean of 10 years and standard deviation of 2 years. The manufacturer has budgeted $5000 per batch to support the warranty on its speakers that were produced in batches of 1,000. How long a warranty period can be offered given that the cost of repairing or replacing a speaker is $50 per unit. Use z table