Question

Single adults: According to a Pew Research Center analysis of census data, in 2012, 20% of American adults ages 25 and older had never been married. (Source: Wang, W., and Parker, K. (2014). Record Share of Americans Have Never Been Married. Pew Research Center.)

For a random sample of 50 adults, what is the probability that the more than 21% of adults age 25 and older had never been married? Enter your answer in decimal form rounded to three decimal places.

Answer 1

To find the probability that more than 21% of adults age 25 and older had never been married in a random sample of 50 adults, we can use the binomial probability formula. The probability is approximately 0.660.

Step-by-step explanation:

To find the probability that more than 21% of adults age 25 and older had never been married out of a random sample of 50 adults, we can use the binomial probability formula. The formula is P(X > k) = 1 - P(X <= k), where X is the number of successes (adults who have never been married) in the sample, and k is the desired value (in this case, 21% of 50). To solve this, we need to calculate P(X <= k) and subtract it from 1.

First, we convert the percentage to a decimal: 21% = 0.21. Then, we use the binomial probability formula with n = 50, p = 0.21, and k = 0, 1, 2, ..., 50 to calculate the cumulative probability of getting a value less than or equal to k. Finally, we subtract this cumulative probability from 1 to find P(X > k).

Using a calculator or a statistical software, the probability that more than 21% of adults age 25 and older had never been married in a random sample of 50 adults is approximately 0.660.