Answer: 0.2224
Step-by-step explanation:
Given: The proportion of adults need eye correction: p= 78%=0.78
Let X be a binomial variable that represents the number of adults who need eye correction.
Sample size of adults: n= 12
Binomial ditsribution formula:
[tex]P(X=x)=^nC_xp^x(1-p)^{n-x}[/tex]
Now, the probability that at least 11 of them need correction for their eyesight will be
[tex]P(X\geq11)=P(X=11)+P(X=12)\\\\=^{12}C_{11}(0.78)^{11}(1-0.78)^{1}+^{12}C_{12}(0.78)^{12}(1-0.78)^{0}\\\\=(12)(0.78)^{11}(0.22)+(1)(0.78)^{12}(1)\\\\\approx0.1716503+0.05071486=0.22236516\approx0.2224[/tex]
Hence, the required probability = 0.2224
