Question

The 2018 Current Population Survey (CPS) estimates that 19.7% of Mississippians live in poverty, which makes Mississippi the state with the highest poverty rate in the United States. If we take a random sample of 250 Mississippians, what is the probability that at least 25% of them live in poverty?

Answer 1

Answer: 0.0265

Explanation:

Given: The proportion of Mississippians live in poverty, which makes Mississippi the state with the highest poverty rate in the United States. : p = 19.7% = 0.197

Sample size : n= 250

The probability that at least 25% of them live in poverty will be

`P(\hat{p}\geq0.25)=P(\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}\geq\frac{0.25-0.197}{\sqrt{(0.25*0.75)/(250)}})\\\\=P(Z>\geq1.9353)\\\\=1-P(Z<1.935)\\\\=1-0.9735\ \ \ \ [\text{By p-value table}]\\\\=0.0265`

Hence, the required probability = 0.0265