Question

evaluate (sigma=sqrt{np(1 - p)}) for (n = 1575), (p=\frac{1}{2}). (sigma=square) (simplify your answer. type an integer or decimal rounded to one decimal place as needed.)

Explanation:

Step1: Substitute values into formula

Given \(n = 1575\), \(p=\frac{1}{2}\), then \(1 - p=1-\frac{1}{2}=\frac{1}{2}\).
The formula is \(\sigma=\sqrt{np(1 - p)}\), substituting we get \(\sigma=\sqrt{1575\times\frac{1}{2}\times\frac{1}{2}}\).

Step2: Simplify the expression inside the square - root

First, calculate \(1575\times\frac{1}{2}\times\frac{1}{2}=\frac{1575}{4}=393.75\).
Then \(\sigma=\sqrt{393.75}\).

Step3: Calculate the square - root

\(\sqrt{393.75}\approx19.8\)

Answer:

\(19.8\)