Answer with explanation:
The binomial distribution formula :-
[tex]P(X=x)=^nC_x\ p^x\ (1-p)^{n-x}[/tex], where P(x) is the probability of getting success in x trials , n is total number of trials and p is the probability of getting success in each trial.
Given : The probability that adults need correction for their eyesight = 0.84
If 22 adults are randomly selected, then the probability that no more than 1 of them need correction for their eyesight .
[tex]P(X\leq1)=P(0)+P(1)\\\\=^{22}C_0\ (0.84)^{0}\ (1-0.84)^{22-0}+^{22}C_1\ (0.84)^1\ (1-0.84)^{22-1}\\\\=(0.84)^{0}(0.16)^{22}+22(0.84)(0.16)^{21}=3.6\times10^{-16}[/tex]
which is much lower than 0.5 .
Yes , 1 is significantly low number of adults requiring eyesight correction .
