Answer :
Answer:
0.9039.
Step-by-step explanation:
We have been given that approximately 10.3% of American high school students drop out of school before graduation. Choose 11 students entering high school at random. We are asked to find the probability of no more than 2 dropout.
We will use Bernoulli's trials to solve our given problem as:
[tex]P(X=x)=^nC_x\cdot p^x(1-p)^{n-x}[/tex]
For no more than 2 dropouts, we need to find dropout of 1 student and 2 students as:
[tex]P(X\leq 2)=^{11}C_0\cdot (0.103)^0(1-0.103)^{11-0}+^{11}C_1\cdot (0.103)^1(1-0.103)^{11-1}+^{11}C_2\cdot (0.103)^2(1-0.103)^{11-2}[/tex]
[tex]P(X\leq 2)=1\cdot (1)(0.897)^{11}+11\cdot (0.103)^1(0.897)^{10}+55\cdot (0.103)^2(0.897)^{9}[/tex]
[tex]P(X\leq 2)=0.3024940757+11\cdot (0.103)(0.3372286239)+55\cdot (0.010609)(0.375951643)[/tex]
[tex]P(X\leq 2)=0.3024940757+0.3820800308787+0.219365903932285[/tex]
[tex]P(X\leq 2)=0.903940010510985[/tex]
[tex]P(X\leq 2)\approx 0.9039[/tex]
Therefore, the probability of no more than 2 dropout is 0.9039.