Question

evaluate \\( \sigma = \sqrt { n p ( 1 - p ) } \\) for \\( n = 1471, p = \frac { 2 } { 5 } \\).
\\( \sigma = \square \\)
(simplify your answer. type an integer or decimal rounded to one decimal place as needed.)

Explanation:

Step1: Substitute values

Substitute \(n = 1471\), \(p=\frac{2}{5}\), and \(1 - p=1-\frac{2}{5}=\frac{3}{5}\) into the formula \(\sigma=\sqrt{np(1 - p)}\).
So, \(\sigma=\sqrt{1471\times\frac{2}{5}\times\frac{3}{5}}\).

Step2: Calculate the product inside the square - root

First, calculate \(1471\times\frac{2}{5}\times\frac{3}{5}=\frac{1471\times2\times3}{5\times5}=\frac{8826}{25}=353.04\).

Step3: Take the square - root

\(\sigma=\sqrt{353.04}\approx18.8\)

Answer:

\(18.8\)