Question

check here for instructional material to complete this problem.
evaluate the formula ( z = \frac { overline { x } - mu } { \frac { sigma } { sqrt { n } } } ) when ( mu = 115 ), ( n = 18 ), ( overline { x } = 120 ), and ( sigma = 3 ).
( z = ) (round to three decimal places as needed.)

Explanation:

Step1: Substitute the values into the formula

Substitute \(\mu = 115\), \(\bar{x}=120\), \(\sigma = 3\), and \(n = 18\) into \(z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\).

$$z=\frac{120 - 115}{\frac{3}{\sqrt{18}}}$$

Step2: Simplify the denominator

First, calculate \(\sqrt{18}\approx4.2426\), then \(\frac{3}{\sqrt{18}}=\frac{3}{4.2426}\approx0.7071\).

Step3: Calculate the numerator

The numerator is \(120 - 115=5\).

Step4: Calculate the value of \(z\)

Now, \(z=\frac{5}{0.7071}\approx7.071\)

Answer:

\(7.071\)