Question

In the United States, 75 percent of adults wear glasses or contact lenses. A random sample of 10 adults in the United States will be selected.

What is closest to the probability that fewer than 8 of the selected adults wear glasses or contact lenses?

Answer 1

0.4745 is the probability that fewer than 8 of the selected adults wear glasses or contact lenses.

Explanation:

We are given the following information:

We treat adult adults wear glasses or contact lenses as a success.

P(Adults wear glasses or contact lenses) = 75% = 0.75

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 = 10

We have to evaluate:

P(fewer than 8 of the selected adults wear glasses or contact lenses)

`P(x < 8)\\=1 - P(x = 8) - P(x = 9) - P(x = 10)\\=1 - \binom{10}{8}(0.75)^8(1-0.75)^2 - \binom{10}{9}(0.75)^9(1-0.75)^1- \binom{10}{10}(0.75)^10(1-0.75)^0\\=1 - 0.2815-0.1877-0.0563\\= 0.4745`

0.4745 is the probability that fewer than 8 of the selected adults wear glasses or contact lenses.