Exercise $16-35$ Static $($Using Excel$)$

Following an exponential distribution, the average lifespan of a smartphone battery is $2\mathrm{.}3$ years. The battery manufacturer wants to

offer a warranty for its customers to receive a free replacement if the battery fails during the first year. Each battery generates a profit

of $$10\mathrm{.}85,$ and the replacement cost is $$6\mathrm{.}35.$ Use Excel's Analysis ToolPak, with a seed of $1,$ to develop a Monte Carlo simulation for

the lifespan of $100$ batteries.

a$.$ What is the expected total cost of this warranty program?

Note: Round intermediate calculations to at least $4$ decimal places and your final answer to $2$ decimal places.

b$.$ In order to cover the cost of the warranty program, how many additional battery units does the company need to sell?

Note: Round intermediate calculations to at least $4$ decimal places and your final answer to $2$ decimal places.