Question

evaluate ( z=\frac{x-mu}{sigma} ) if ( x = 181, mu = 170 ), and ( sigma = 8 ).
( z=square )
(type an integer or decimal rounded to two decimal places as needed.)

Explanation:

Step1: Substitute the values into the formula

Given \(x = 181\), \(\mu=170\), and \(\sigma = 8\), substitute into \(z=\frac{x-\mu}{\sigma}\).

$$z=\frac{181 - 170}{8}$$

Step2: Calculate the numerator

$$181-170 = 11$$

So the formula becomes \(z=\frac{11}{8}\).

Step3: Perform the division

$$z=\frac{11}{8}=1.375$$

Rounding \(1.375\) to two decimal places gives \(1.38\).

Answer:

\(1.38\)