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

Question

2 months ago

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

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

Mathematics

1 answer:

tester [12.3K] · Answer 1 · 2026-02-27T00:04:57+03:00

Response:

The likelihood that fewer than 8 of the sampled adults use glasses or contact lenses is 0.4745.

Detailed explanation:

We have the following information:

Considering adults wearing glasses or contact lenses a success.

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

Hence, the number of adults follows a binomial distribution, represented as:

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

with n as total observations, x as successful outcomes, and p as success probability.

For our case, n = 10

We need to calculate:

P(fewer than 8 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 of having fewer than 8 of the selected adults utilizing glasses or contact lenses.