Question

Assume that when an adult is randomly​ selected, the probability that they do not require vision correction is 28% If 12 adults are randomly​ selected, find the probability that fewer than 4 of them do not require a vision correction.

If 12 adults are randomly​ selected, the probability that fewer than 4 of them do not require a vision correction is ________

Answer 1

Solution:

Given:

p = probability that an adult do not require vision correction = 0.28

thus q = 1 - p = 1 - 0.28 = 0.72

n = sample size = 12

We have to find:

P( Fewer than 4 of them do not require a vision correction ) = ............?

That is:

P( X < 4) = ............?

   Here X = number of an adult do not require vision correction follows a Binomial distribution with parameters n = 12 and p = 0.28

Formula:

where

Thus

P( X < 4) = P(X = 0) + P( X = 1) + P( X = 2 ) + P ( X = 3)

Thus find each probability separately by using binomial probability formula:

Thus

P( X < 4) = P(X = 0) + P( X = 1) + P( X = 2 ) + P ( X = 3)

P( X < 4) = 0.0194084 + 0.0905726 + 0.1937247 + 0.2511246

P( X < 4) = 0.5548303

P( X < 4) = 0.5548

Thus the probability that fewer than 4 of them do not require a vision correction is 0.5548