Answer:
0.121 is the probability that at least 15 of them need correction for their eyesight
Step-by-step explanation:
We are given the following information:
We treat adult needing an correction as a success.
P(Adult need eye correction) = 79% = 0.79
Then the number of adults follows a binomial distribution, where
[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]
where n is the total number of observations, x is the number of success, p is the probability of success.
Now, we are given n = 16 and x = 15
We have to evaluate:
[tex]P(x \geq 15) = P(x = 15) + P(x = 16) \\= \binom{16}{15}(0.79)^15(1-0.79)^1 + \binom{16}{16}(0.79)^16(1-0.79)^0\\= 0.0978 + 0.0230\\= 0.121[/tex]
No, 15 is not a large number as the the probability for at least 15 adults to have eye correction is 12% approximately, which is not so small.
