Question

evaluate ( z=\frac{overline{x}-mu}{\frac{sigma}{sqrt{n}}} ) if ( overline{x}=29.6, mu=54.9, sigma=3.5 ), and ( n=64 ).
( z=square )
(type an integer or decimal rounded to two decimal places as needed.)

Explanation:

Step1: Substitute the values into the formula

Given \(z=\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\), substitute \(\overline{x} = 29.6\), \(\mu=54.9\), \(\sigma = 3.5\), and \(n = 64\).

$$z=\frac{29.6 - 54.9}{\frac{3.5}{\sqrt{64}}}$$

Step2: Simplify the denominator

First, calculate \(\sqrt{64}=8\). Then \(\frac{3.5}{\sqrt{64}}=\frac{3.5}{8}=0.4375\).

Step3: Simplify the numerator

\(29.6-54.9=-25.3\)

Step4: Calculate the value of \(z\)

$$z=\frac{-25.3}{0.4375}=-57.83$$

Answer:

\(-57.83\)