Auto batteries have an average life of $2\mathrm{.}7$ years. Battery life is normally distributed with a mean of $2\mathrm{.}7$ years and a standard deviation of $0\mathrm{.}4$ years. The batteries are warranted to operate for a minimum of $2$ years. If a battery fails within the warranty period, it will be replaced with a new battery at no charge. The company sells and installs the batteries. Also, the usual $$3$ installation charge will be waived.

Use and Table B$.$

a$.$ What percentage of batteries would you expect to fail before the warranty period expires? $($Round your z value to $2$ decimal places. Round probabilities to $4$ decimal places. Round your final answer to $2$ decimal places.$)$

b$.$ A competitor is offering a warranty of $31$ months on its premium battery. The manager of this company is toying with the idea of using the same battery with a different exterior, labeling it as a premium battery, and offering a $31-$month warranty on it$.$ What percentage of the batteries would you expect to fail before this new warranty period expires? $($Round your z value to $2$ decimal places. Round probabilities to $4$ decimal places. Round your final answer to $2$ decimal places.$)$