According to government data, 22 percent of children in the United States under the age of 6 years live in households with incomes that are classified at a particular income level. A simple random sample of 300 children in the United States under the age of 6 years was selected for a study of learning in early childhood. If the government data are correct, which of the following best approximates the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level? (Note: \(z\) represents a standard normal random variable.)

Summary Submit Skip Question

Using the formulas:

$$ \text{Standardized test statistic} = \frac{\text{statistic}-\text{parameter}}{\text{standard error of the statistic}} $$ $$ \text{standard error of the statistic (for one population) } = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} $$ $$ z = \frac{0.27-0.22}{\sqrt{\frac{(0.22)(1-0.22)}{300}}} $$