Question

2a. According to a Pew Research survey, about 25% of American adults are pessimistic about the future of marriage and the family. This is based on a sample, but assume this percentage is correct for all American adults. What is the probability that in a sample of 20 American adults, 23% or fewer of the people in the sample are pessimistic about the future of marriage and family

Answer 1

Answer: 0.4181807

Step-by-step explanation:

Probability that American adults are pessimistic about the future of marriage and the family: p= 0.25

Sample size n= 20

Let $\hat{p}$ be the sample proportion of American adults that are pessimistic about the future of marriage and the family.

$P(\hat{p}\leq0.23)=P(\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

Hence, the required probability = 0.4181807