Question

A survey showed that 84​% of adults need correction​ (eyeglasses, contacts,​ surgery, etc.) for their eyesight. If 22 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 22 adults require eyesight correction is nothing. ​(Round to three decimal places as​ needed.)

Answer 1

Solution:

Given:

p = Probability of adults need correction​ (eyeglasses, contacts,​ surgery, etc.) for their eyesight = 84% = 0.84

thus q = 1 - p = 1 - 0.84 = 0.16

n = Number of adults are randomly​ selected = 22

We have to find: the probability that no more than 1 of them need correction for their eyesight.

That is:

Here X = Number of adults need correction​ for their eyesight follows a Binomial distribution with n = 22 and p = 0.84

Thus using Binomial probability formula we get:

where

Thus

Find P(X = 0) and P(X=1)

and

Thus

Thus the probability that no more than 1 of them need correction for their eyesight is 0.000

Is 1 a significantly low number of adults requiring eyesight​ correction?

Yes , since probability of 1 of them need correction for their eyesight is 0.000 < 0.05 or less than 5%.