Answer: 0.9526
Step-by-step explanation:
Binomial probability formula to find the probability of getting success in x trial :-
[tex]P(x)=^nC_xp^x(1-p)^x[/tex], where p is the probability of success and n is the sample size .
Given : The probability of a potential employee passing a training course is 86%.
i.e. p=0.86
Sample size : n=15
Then, the probability that more than "11" will pass the test:-
[tex]P(x\geq11)=P(11)+P(12)+P(13)+P(14)+P(15)\\\\=^{15}C_{11}(0.86)^{11}(0.14)^{4}+^{15}C_{12}(0.86)^{12}(0.14)^{3}+^{15}C_{13}(0.86)^{13}(0.14)^{2}+^{15}C_{14}(0.86)^{14}(0.14)^{1}+^{15}C_{15}(0.86)^{15}(0.14)^{0}\\\\=\dfrac{15!}{11!4!}(0.86)^{11}(0.14)^{4}+\dfrac{15!}{12!3!}(0.86)^{12}(0.14)^{3}+\dfrac{15!}{13!2!}(0.86)^{13}(0.14)^{2}+(15)(0.86)^{14}(0.14)^{1}+(1)(0.86)^{15}(0.14)^{0}\\\\=0.952154074749\approx0.9526[/tex]
Hence, the probability that more than "11" will pass the test =0.9526
