A manufacturer of programmable calculators is attempting to determine a reasonable free$-$service period for a model it will introduce shortly. The manager of product testing has indicated that the calculators have an expected life of $90$ months. Assume product life can be described by an exponential distribution.

$\backslash$table$[[$T MTBF$,\frac{e^{-T}}{?}$ MTBF$,\frac{T}{?}$ MTBF$,\frac{e^{-T}}{?}$ MTBF$,\frac{T}{?}$ MTBF$,\frac{e^{-T}}{?}$ MTBF$],[0\mathrm{.}10,0\mathrm{.}9048,2\mathrm{.}60,0\mathrm{.}0743,5\mathrm{.}10,0\mathrm{.}0061],[0\mathrm{.}20,0\mathrm{.}8187,2\mathrm{.}70,0\mathrm{.}0672,5\mathrm{.}20,0\mathrm{.}0055],[0\mathrm{.}30,0\mathrm{.}7408,2\mathrm{.}80,0\mathrm{.}0608,5\mathrm{.}30,0\mathrm{.}0050],[0\mathrm{.}40,0\mathrm{.}6703,2\mathrm{.}90,0\mathrm{.}0550,5\mathrm{.}40,0\mathrm{.}0045],[0\mathrm{.}50,0\mathrm{.}6065,3\mathrm{.}00,0\mathrm{.}0498,5\mathrm{.}50,0\mathrm{.}0041],[0\mathrm{.}60,0\mathrm{.}5488,3\mathrm{.}10,0\mathrm{.}0450,5\mathrm{.}60,0\mathrm{.}0037],[0\mathrm{.}70,0\mathrm{.}4966,3\mathrm{.}20,0\mathrm{.}0408,5\mathrm{.}70,0\mathrm{.}0033],[0\mathrm{.}80,0\mathrm{.}4493,3\mathrm{.}30,0\mathrm{.}0369,5\mathrm{.}80,0\mathrm{.}0030],[0\mathrm{.}90,0\mathrm{.}4066,3\mathrm{.}40,0\mathrm{.}0334,5\mathrm{.}90,0\mathrm{.}0027],[1\mathrm{.}00,0\mathrm{.}3679,3\mathrm{.}50,0\mathrm{.}0302,6\mathrm{.}00,0\mathrm{.}0025],[1\mathrm{.}10,0\mathrm{.}3329,3\mathrm{.}60,0\mathrm{.}0273,6\mathrm{.}10,0\mathrm{.}0022],[1\mathrm{.}20,0\mathrm{.}3012,3\mathrm{.}70,0\mathrm{.}0247,6\mathrm{.}20,0\mathrm{.}0020],[1\mathrm{.}30,0\mathrm{.}2725,3\mathrm{.}80,0\mathrm{.}0224,6\mathrm{.}30,0\mathrm{.}0018],[1\mathrm{.}40,0\mathrm{.}2466,3\mathrm{.}90,0\mathrm{.}0202,6\mathrm{.}40,0\mathrm{.}0017],[1\mathrm{.}50,0\mathrm{.}2231,4\mathrm{.}00,0\mathrm{.}0183,6\mathrm{.}50,0\mathrm{.}0015],[1\mathrm{.}60,0\mathrm{.}2019,4\mathrm{.}10,0\mathrm{.}0166,6\mathrm{.}60,0\mathrm{.}0014],[1\mathrm{.}70,0\mathrm{.}1827,4\mathrm{.}20,0\mathrm{.}0150,6\mathrm{.}70,0\mathrm{.}0012],[1\mathrm{.}80,0\mathrm{.}1653,4\mathrm{.}30,0\mathrm{.}0136,6\mathrm{.}80,0\mathrm{.}0011],[1\mathrm{.}90,0\mathrm{.}1496,4\mathrm{.}40,0\mathrm{.}0123,6\mathrm{.}90,0\mathrm{.}0010],[2\mathrm{.}00,0\mathrm{.}1353,4\mathrm{.}50,0\mathrm{.}0111,7\mathrm{.}00,0\mathrm{.}0009],[2\mathrm{.}10,0\mathrm{.}1255,4\mathrm{.}60,0\mathrm{.}0101,,],[2\mathrm{.}20,0\mathrm{.}1108,4\mathrm{.}70,0\mathrm{.}0091,,],[2\mathrm{.}30,0\mathrm{.}1003,4\mathrm{.}80,0\mathrm{.}0082,,],[2\mathrm{.}40,0\mathrm{.}0907,4\mathrm{.}90,0\mathrm{.}0074,,],[2\mathrm{.}50,0\mathrm{.}0821,5\mathrm{.}00,0\mathrm{.}0067,,]]$

a$.$ If service contracts are offered for the expected life of the calculator, what percentage of those sold would be expected to fail during the service period? $($Round your answer to $4$ decimal places.$)$

$1---$T$/$MTBF