Question

evaluate ( z=\frac{x-mu}{sigma} ) if ( x = 69, mu = 74.2 ), and ( sigma = 2.3 ).
( z=square )
(type an integer or decimal rounded to two decimal places as needed.)

Explanation:

Step1: Substitute the values into the formula

Substitute \(x = 69\), \(\mu=74.2\), and \(\sigma = 2.3\) into the formula \(z=\frac{x - \mu}{\sigma}\).

$$z=\frac{69 - 74.2}{2.3}$$

Step2: Calculate the numerator

Calculate \(69-74.2=- 5.2\).

$$z=\frac{-5.2}{2.3}$$

Step3: Calculate the value of \(z\)

Divide \(-5.2\) by \(2.3\). \(-5.2\div2.3\approx - 2.26\) (rounded to two decimal places)

Answer:

\(-2.26\)