Question

The Census Bureau reports that 82% of Americans over the age of 25 are high school graduates. A survey of randomly selected residents of certain county included 1400 who were over the age of 25, and 1120 of them were high school graduates.(a) Find the mean and standard deviation for the number of high school graduates in groups of 1400 Americans over the age of 25. Mean = Standard deviation =(b) Is that county result of 1120 unusually high, or low, or neither?

Answer 1

`\begin{gathered} \text{The mean for the groups of 1400 is} \\ \\ (1400)\cdot(82\%)\Rightarrow(1400)(0.82) \\ =1148 \end{gathered}`
`\begin{gathered} \text{The standard deviation} \\ \sqrt[]{(0.82)(1-0.82)(1400)} \\ =\sqrt[]{(0.82)(0.18)(1400)} \\ =\sqrt[]{206.64} \\ =14.37 \end{gathered}`

Is that county result of 1120 unusually high, low, or neither?

1148 - 2(14.37) = 1119.26

It is neither as it is within 2 standard deviation from the mean 1148.