Consider a set of data in which the sample mean is 49.4
and the sample standard deviation is 5.4
. Calculate the z-score given that x=48.4
. Round your answer to two decimal places.
To calculate the z-score, we use the formula:
\( z = \frac{x - \bar{x}}{s} \)
Where:
\( x = 48.4 \) (the value we want to find the z-score for)
\( \bar{x} = 49.4 \) (the sample mean)
\( s = 5.4 \) (the sample standard deviation)
Plugging in the values:
\( z = \frac{48.4 - 49.4}{5.4} \)
\( z = \frac{-1}{5.4} \)
\( z = -0.19 \)
Therefore, the z-score for x=48.4 is -0.19.