Following an exponentlal 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 recelve a free replacement if the battery falls 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 $100$ batterles.

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

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

The expected total cost of the warranty program for every $100$ batteries sold

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

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

Additional batteries the company needs to sell for every $100$ batteries currently sold