Question

A survey showed that 79​% of adults need correction​ (eyeglasses, contacts,​ surgery, etc.) for their eyesight. If 16 adults are randomly​ selected, find the probability that at least 15 of them need correction for their eyesight. Is 15 a significantly high number of adults requiring eyesight​ correction?

Answer 1

0.121 is the probability that at least 15 of them need correction for their eyesight

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

`P(X=x) = \binom{n}{x}.p^x.(1-p)^(n-x)`

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:

`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`

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.