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

Answer 1

To find the probability that fewer than 8 adults wear glasses or contact lenses, we can use the binomial distribution formula. Calculate the individual probabilities for 0, 1, 2, 3, 4, 5, 6, and 7 adults wearing glasses or contact lenses, and add them together.

Step-by-step explanation:

To find the probability that fewer than 8 of the selected adults wear glasses or contact lenses, we need to calculate the probability of 0, 1, 2, 3, 4, 5, 6, and 7 adults wearing glasses or contact lenses and then add them together. We can use the binomial distribution formula to calculate each individual probability. The formula is:

P(x) = (nCx) * p^x * (1-p)^(n-x)

where:

P(x) is the probability of x adults wearing glasses or contact lenses

n is the number of trials (10)

x is the number of successes (0, 1, 2, 3, 4, 5, 6, or 7)

p is the probability of success (0.75)

After calculating the individual probabilities, we can add them together to find the probability that fewer than 8 adults wear glasses or contact lenses.