Question

A survey showed that 72​% of adults need correction​ (eyeglasses, contacts,​ surgery, etc.) for their eyesight. If 19 adults are randomly​ selected, find the probability that no more than 1 of them need correction for their eyesight. Is 1 a significantly low number of adults requiring eyesight​ correction?

The probability that no more than 1 of the 19 adults require eyesight correction is ____

Answer 1

Let X denotes the number of adults who need correction​ (eyeglasses, contacts,​ surgery, etc.) for their eyesight among 19 randomly selected adults.

Here,

X ~ Binomial(n = 19, p = 0.72)

The probability mass function of X is

Now,

The probability that no more than 1 of them need correction for their eyesight

Since the probability is close to 0, so 1 is a significantly low number of adults requiring eyesight​ correction.