Question 1137335
<b>(a) exactly 18 will have a useful life of at least 800 hours</b>
<pr>
{{{(0.9)^18 * (0.1)^2 * (20!/(18!*2!))}}} = 0.2852
<pr>
<b>(b) at least 15 will have a useful life of at least 800 hours</b>
<pr>
P(exactly 15 with useful life of at least 800 hours) = {{{(0.9)^15 * (0.1)^5 * (20!/(15!*5!))}}} = 0.0319
P(exactly 16 with useful life of at least 800 hours) = {{{(0.9)^16 * (0.1)^4 * (20!/(16!*4!))}}} = 0.0898
P(exactly 17 with useful life of at least 800 hours) = {{{(0.9)^17 * (0.1)^3 * (20!/(17!*3!))}}} = 0.1901
P(exactly 18 with useful life of at least 800 hours) = {{{(0.9)^18 * (0.1)^2 * (20!/(18!*2!))}}} = 0.2852
P(exactly 19 with useful life of at least 800 hours) = {{{(0.9)^19 * (0.1)^1 * (20!/(19!*1!))}}} = 0.2702
P(exactly 20 with useful life of at least 800 hours) = {{{(0.9)^20}}} = 0.1216
<pr>
P(at least 15 will have a useful life of at least 800 hours) = 0.0319 + 0.0898 + 0.1901 + 0.2852 + 0.2702 + 0.1216 = 0.9888