Question

An observation was drawn from a normally distributed population with mean 2.397 and standard deviation 0.612. If the observed value is 3.144, find the z-score. Give your answer accurate to 3 decimal places (Example: 4.567).

Answer 1

Answer:

1.221

Step-by-step explanation:

We have been given that an observation was drawn from a normally distributed population with mean 2.397 and standard deviation 0.612. We are asked to find the z-score of an observed value of 3.144.

We will use z-score formula to solve our given problem.

$z=\frac{x-\mu}{\sigma}$, where,

z = Z-score,

x = Sample score,

$\mu$ = Mean,

$\sigma$ = Standard deviation.

Upon substituting our given values in z-score formula, we will get:

$z=\frac{3.144-2.397}{0.612}$

$z=\frac{0.747}{0.612}$

$z=1.2205882352941176$

Round to three decimal places, we will get:

$z\approx 1.221$

Therefore, our required z-score would be 1.221.