Question

A 2015 study conducted by the National Center for Health Statistics found that 51% of U.S. households had no landline service. This raises concerns about the accuracy of certain surveys, as they depend on random-digit dialing to households via landlines. Researchers pick eleven U.S. households at random. Complete parts a through c. a) What is the probability that all eleven of them have a landline?

Answer 1

The probability that all eleven randomly selected U.S. households have a landline is approximately 0.006.

Step-by-step explanation:

To find the probability that all eleven U.S. households have a landline, we can use the given information that 51% of U.S. households had no landline service. This means that 49% of U.S. households do have a landline.

Since the researcher randomly selects eleven U.S. households, the probability that each household has a landline is 49% or 0.49.

To find the probability that all eleven households have a landline, we multiply the probabilities of each household having a landline:

P(all eleven households have a landline) =

`(0.49)^1^1`

≈ 0.006